If you got the right hooks it would be just fine :) porch swings can hang on hooks and a chian and the hooks are not that big.

Most hooks in packages have weight limets on them unless you are worried the frame will fall apart.

You could also put two nails on the wall and set the fame on them to take some of the weight off the hooks and chain.

It's going to look beautiful. I'm thinking a nice wood stain would show it off more, but then again I'm not an expert. Wait to see what someone who knows what they are talking about, says.

I am no expert, but stained glass is one of my many hobbies.
Go to www.glasscrafters.com and look up CH-1 --- sidemount hooks.
Glass pieces such as these are best hung with mounts on the side. It distributes the weight better -- especially if the piece is framed in zinc or brass and not wood. You have a substantial wood frame, so you should be fine. 7# is not a lot, but it is still a good amount of weight to having gravity pulling on it. You can probably buy a similar hardware. My suggestion is a hanger that has two screws, then chain, then make sure the eye hooks or whatever hooks you choose are securely in the frame above.
It looks like you are planning to hang this in the door between the two rooms? Beautiful!! I have a piece hanging between my kitchen and family room. It was a real find - although I had to take it apart and do a rebuild! I think the frame would look beautiful darker - but that would depend on what is currently on the frame - i.e., a poly.
I have also seen this done where you would wrap a chain around the entire piece - but I don't think that is necessary - you do have 4', but it is only 12" ----
and if you can't do it ------ I will give you my address and would be glad to take it off your hands!!!

Thanks for all your replies.

koidom-
You're right, it is the frame that I'm worried about. It's the original frame
that was used when the window was hung so it's pretty old. Resting the window
on nails/screws protruding from the wall is a good idea. I remember seeing a setup
similar to this in art galleries where some sort of metal is screwed on the wall
and on the sides of modern metal sculptures so that the artwork appears to be
floating.

brutuses-
Thanks. The stained glass in the window complements both room colors, I think it
would really look lovely in that doorway. I am now leaning towards staining the
frame to a dark color.

no-green-thumb-
Thanks for the link. I'll take a look at those sidemount hooks.

The stained glass has 2 metal bars running along its height that are strategically
placed so that it does not fight with the overall appearance. I suppose the
bars give additional support to the frame. It also has some kind of putty that
holds it in place against the frame and some of it have already chipped -- I'd
say about 97% of the putty is still intact. The leading has powdery stuff in some
places. Does it sound like it needs to be rebuilt? Is this difficult to do?
How much do you think am I looking at to have this be done by a professional?

I really hope you don't mind my questions. I just thought you might be able to
give useful insights since you rebuilt a stained glass panel before.

Lovely piece, and lovely home! I would paint the frame the same color as the trim in the doorway. I think it would enhance the 'transom' effect that this piece will give in that spot. It will also let the glass be the focus rather than the contrast of the stained frame to the surrounding doorway. I think it will enhance the colors, too, which look like they are a perfect choice with your room colors.

the vertical bars are called rebar - and it almost sounds like overkill in a piece of that size - nonetheless, it is additional reinforcement.
The putty that is used is to keep the glass from rattling in the channels. It does not serve a constructive type purpose.
To rebuild, you are probably looking at a couple of hundred dollars at least, maybe more, and it doesn't look like it needs a rebuild. The pieces are not broken.
The dust can be oxidation or lead dust.
Do not use windex or any other ammonia type product - it will further deteriorate the putty.
Take it outside, put on a respirator and take some very fine steel wool to the lead channels. You will also see where the channels have been soldered together. Those areas may have more oxidation.
After scrubbing it with steel wool, you can wipe it off with water. Then take some car wax - anything with carnuba wax - and put it on the lead channels. Then when you polish it off, you will polish the wax as well.
Unless you have done this before, I would not take it out of the frame. Glass has a lot of bend and you will probably crack pieces. It sounds like it was well-built, just needs some cleaning up. But please beware of the lead dust. You don't want to breathe that stuff in.
I don't mean to scare you ----- it is not hard at all --- again, just sounds like it needs some cleaning.
I personally don't see it against a wall. Glass needs to have light coming through it.
Come back with more questions ---- I don't know much about decorating -- and am usually here with more questions than answers. I am thrilled to be able to help someone!!

If it were mine, I'd make a frame across the doorway to set the framed stain glass piece in as if it were built into the home. I'd use a tung oil finish to give it's wood frame a hand rubbed look and not hurt the value of the piece as a unit. I think painting it would devalue it.

Anyway here's a virtual to give you an idea of what I'm talking about. Ofcourse it depends on the sizes of the transom and door opening whether you'll need to add pieces on the sides or not. I didn't ad them in my virtual.

{{!gwi}}

I should have said dust mask - a good dust mask will work for what you need to do - and use 0000 steel wool.
I do like the built-in idea as well as Les's suggestion.
I would think OP would need to measure the height of the doorway - looks like higher than 8' ceilings, but I could be wrong.
Typically, when pieces are installed in a transom, there is not a frame built around it. The piece is built to the appropriate size, then put in and held in place with quarter round or other type of molding - I am wondering if maybe it was taken out and then framed - or maybe it was never actually installed - just hung. I personally wouldn't be concerned about devaluing the piece.
In any event, it does look like a well-made piece with the wide frame and the rebar. Whatever OP does will work.
I am also thinking in the living room, if the center window is wide enough taking the curtain down and hanging it in that window.
I wonder how old it is. A lot of very old pieces warp and sag because of the weight and then pieces crack. I picked up my window at an antique store I frequent. This particular dealer doesn't get many in because of the high cost of repair. It is extremely time-consuming.

Lots of great ideas. Thanks everyone. I will post some pictures
when I it's done. I feel it's just fair after all the help you
have given.

les917-
Just when I'm pretty sure that staining the frame is the way I'm
going... you make this great point! Thanks for the input.

justgotabme-
Thanks so much for the virtual. I have to consider this too.
It looks fantastic. Seeing it makes me more enthusiastic to get
on and finish this project!

The width of the doorway is 5ft. I measured the frame last night
and it turns out that it is really 17in by 56in (that's including the
wood frame) so I have 2 inches of space to deal with on each side.

no-green-thumb-
It's a relief to know that rebuilding would not be necessary, I
don't think I'm up to doing it myself, anyway. Cleaning it, however,
is right up my alley. I really appreciate it that you took time to
explain the process to me.

I realize that I was not clear when I wrote about using nails/screws
for additional support. I meant to say that the nails/screws would
be attached to the facing sides of the doorway frame (not wall). I
don't intend to hang the glass against a wall.

The doorway height is just over 8 ft tall. So I will have to use a
very short chain to hang it or do what justgotabme suggested.

I have no idea about the age of the glass. I really bought it because
of the glass colors. It's really beautiful. The seller said that it
was salvaged from an old house that was torn down and that the frame
might be the actual window frame. Sounds like she's not sure about
the frame either. The frame does not appear to have any holes to
indicate that it was hung from a chain.

Here are more details:

We had a carpenter make a substantial frame for ours when we had it. (Now belongs to a son because I could find nowhere to use it in this house due to "open floor plant" which limits a lot of possibilities. He framed it and put it in just like Justgotabeme has depicted. We kept ours in place at the other house for about 7 years with no problems.