It is most likely parsley. Pick off a leaf and smell it.

Looks like Italian parsley to me.

Yes -- it does look like italian parsley to me as well.

However... !

If you're not sure what it is, don't eat it until you've made a positive identification. The parsley/carrot family has a number of useful, edible members and a number of deadly members, and many plants look similar. Probably the most famous of these is poison hemlock, the plant that killed Socrates. While that isn't poison hemlock, I can't positively ID it just from a picture.

If you planted italian parsley, then I'd say it's safe. If you didn't, I'd verify your identification before eating it, just in case.

It looks like Italian parsley, but it is a bit different from mine. Yours has multiple leaves along each stem. Mine has just three leaflets at the end of each stem. I will post a picture when I get home tonight. That is either a different variety of parsley or else something else that only looks like parsley. I would not eat it until you are certain.

Well it's definitely in the parsley/carrot family, I'd say.

There a numerous plants in this family - herbs too.

What do the leaves smell like when crushed? celery? parsley? carrot?

If leaves smell like that of carrots, it may be a weed.

& I think the name of the poisonous plant is Water Hemlock....?

I did an image search for Water Hemlock & it looks quite different from this - this looks very much like some sort of celery - or lovage, perhaps?

Here is a link that might be useful: Google Image - type in the name of a plant to see images of it

The leaves are all in groups of 3.
I picked one and crushed it up, and it smells just like celery.
I planted no carrots, celery, or parsley - this just popped up beside a pepper.
I also noticed that a squirrel or rabbit had eaten a couple bits of it before I put up my chicken wire. They left the peppers, basil, tomatoes, and onions alone - just went for this mysterious growth.
I'm going to assume its celery and re-plant it in a corner of the garden somewhere. We'll see what's left in September!

Hard to see the detail in the stems but from the picture, I vote for celery.

I'd definitely do a smell-test on it.

It's lovage. Smells like celery, and you can use all parts of it like celery, and the seeds can even be used like celery seeds, and it's in the same family as parsley/carrots/ etc. It has umbrella shaped flowers that attract beneficial insects. Best of all, it's a perennial that stays in its place and doesn't wander. Put it in the ground if you can.

The leaves don't look right for lovage; they look more like italian parsley leaves. Celery looks reasonable.

The smell test results are favorable. So is the lack of a skin reaction. Most of the poisonous parsley/carrot family relatives have a somewhat foul, "mousey" smell when crushed. So, that's a good thing :) Animals eating it is also good, but is far from a guarantee; wildlife can eat all sorts of things that are highly toxic to humans.

Carol: Water hemlock is just one. Water hemlock sometimes gets mixed up with angelica. Poison hemlock gets mixed up with queen anne's lace a lot. There are a number of others, like cow parsnip and wild parsnip; I don't have all of the poisonous ones memorized. Two of the general "wild plant safety" rules that I remember are that if it looks like parsley, or looks like an onion but doesn't smell like one, leave it alone unless you can ID it.

I think it is celery. I grow celery this year, it looks just like the ones I have.

Could it be cilantro? Lori

I think it's celery.
Carol

I vote for cilantro!

I vote for wild celery..."cutting celery". Apium graveolens. It's a great substitute for celery.

It is absolutely without a doubt not Poison Hemlock:
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And it is absolutely without a doubt not Cilantro due to above description of smell and leaf shape is totally different:
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It is not Lovage, leaves are not pointed and narrow:
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It is highly unlikely that it is celery because celery seedlings are rare to find at garden centers and a plant so young would probably still have the cotyledons:
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Parsley smells similar to Celery. Parsley does not smell like cilantro at all.
I would bet my Felco Pruners that it is Italian Flatleaf Parsley.
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paulster2626,

Where did you get your pepper plants? Did you start them from seed yourself? Were they seedlings? Did you purchase them from a nursery?

I got them from a garden center - they were seedlings. This thing just popped up right beside the pepper a couple days after planting.

From all those pictures, it looks like parsley to me. I've got a friend who is growing some parsley, so I'll grab a leaf and compare smells.

Smells exactly like celery though.

Thanks for all your help! Didn't know I'd start such a debate...