Door Chime Transformers are generally hardwired to a junction box. What voltage and wattage do you need?

It looks like the plug-in transformer does not have a cord that is permanently attached. If your goal is to hide the transformer and wire, you can still use the plug-in transformer. Transformers need to be accessible, so you can still plug one in at a remote location. Transformers need air circulation, and should not be buried in insulation or placed where to ambient temperature gets too high. To run the wires a longer distance with a low voltage system, you need to consider voltage drop, which means using a larger size wire. The wire also needs to be rated for use inside a wall and being buried in insulation.

Yup, search for door chime transformer. Usually they are connected to a metal box with a knockout.

http://diyhousehelp.com/wp-content/uploads/2013/01/c905k_transformer.jpg

Why would you buy another transformer when the one that it is supplied with is already designed for remote use?

Just hook up the proper length and type of wire to these screws, buy a cheap receptacle and be done with it.

One other thing that comes to mind and this is also keeping in mind that the "rules" for who can legally install low voltage equipment vary from state to state, many like here in WI have no licensing required at the state level, some have a separate low voltage license that can be obtained often with a bit of training, but don't require you to be a licensed master electrician to do so, which I think either way makes sense since few electricians seem to be getting into the growing low voltage landscape lighting biz, or in your case a doorbell and I think it was NJ I heard that recently bumped it down to 10 volts for needing a licensed electrician. (bet the IBEW had a hand in that one!)

Yet, like in my municipality, they do add just a bit in the local codes that specify the system, be it a doorbell, low voltage landscape lighting, etc MUST be tied into the AC power source via a cord and plug going to a legal receptacle and that part would need to be done by a real electrician and if outdoors would need GFCI protection, etc so assuming you're not a licensed electrician, once you choose to hard wire it, you may be crossing over into the "danger zone" and I always mention that for me or anyone I'd think, "getting busted" by the local inspector and paying some fine or double permit fees or something is peanuts compared to IF at some point like after you'd sell the place due to a new job out of town, there's a fire and large $$$ of property damage or God forbid, someone is badly hurt or killed, now YOU have a good chance of being on the WRONG end of a HUGE $$$ lawsuit and even when people say, "oh come on how many doorbells or low volt path lights burn homes down, what if the goofy buyers decide to rewire some stuff and they're idiots! If you've ever seen how ins co's investigate fires with big $$ claims, its very intense and just proving that your probably illegal, hard wired transformer was NOT the cause will likely come at a great expense and hassle to you, assuming you're able to clear your part of it!

RJT, I might has misinterpreted your post, and I don't live there anymore, but as of a couple years ago, a homeowner in WI can do their own wiring.

Depending on the scope of work, the homeowner may need to pull a permit and have the work inspected. But a homeowner can still do their own work.

In WI I did a whole-house gut remodel and replaced the electrical from meter (including the meter) to outlets. Everything was DIY, permitted and inspected. No issues from the town at all. You certainly need to be competent and do neat work, but it can be done.

I now live in CT, CT has pretty much the same rules regarding DIY work in your own home.