looks like a group of baby thatch palms, florida thatch?

Looks like Livistona chinensis (Chinese fan palm) to me, esp. if you purchased in Chicago. They are one of the few palms that are readily available in northern climates.

I agree with bradleyo. Chinese Fan.

Oh wow, so these guys can grow big, huh? Or do they maintain their multi-stemmed, clump-like apprerance indefinitely, if indoors in a small pot? If there are many plants in the same pot, should I be planning to thin them eventually?

Also if anyone has experience with care of these palms, any tips would be appreciated.

Thanks for your help bradleyo & palmshaun! You have no idea how long I looked online trying to find out what this was. I think I was fooled by the juvenile appearance of the plant, so didn't find any species match.

I have no experience with them, but those are actually several plants in the same pot. I don't think you should plan on separating, disturbing the roots would probably not be good. I would think indoors in a pot, they should stay small for a loooooooooong time. I may be wrong but I believe they are exceptionally slow growers in the ground in warm climates. My mom has had one in a 2 gallon sized pot for about 10 years and is very small.

I'm not planning on separating them. I figured they'd stay small, but it's great to have an informed opinion. Thanks bradleyo!

I do wish I had a good photo of my old Chinese fan plam at it's best and before it finally died from being overly rootbound etc. after over ten years of growth, and already in a 21in. pot. One reason, I've NOT replaced it is of course , they can indeed get very big for an indoor situation, and most offered locally are much too crowded with multiples planted per pot, and that's not the best way to grow them. Given more room, some bright light, and allowing some drying between some good soaking, and a little fertilizer, mine went from two in a one gallon pot to the larger of the two having single fronds at least 30in. across in less than ten years, so given some half way decent conditions they aren't slow growing sometimes after
the first couple of years. Mine was much treasured , but much too big for a small house like mine, so when it came time to spend at least fifty dollars to repot one plam, I had to pass on that idea, and it went slowly down hill til it died a few years later. At the time of it's death , and examinging the rootball, there was absollutely no soil to be seen in the rootball and nothing but solid roots with the bottom four or more inches of rootball having many feet of twining roots circling the rootball. When it get's that bad , watering and feeding becomes near impossible, and downwards any plant will go when that rootbound.

I was led to believe that Livistona Chinesis is a single trunk palm with palmate leaves that 'break' quite early.
This palm is multi-trunk and palmate with no sign of the leaves 'breaking'. It is an interesting challenge but I'll work on it.

As your Chinese Fan palms grow, you may want to consider clipping out a few of the smaller seedlings, so that eventually there will only be 3-5 plants left, or even just one. Kinda depends on the look you want to achieve. A single plant will grow larger. Multiple plants will stay smaller.

BTW, when they produce these plants, they just throw a handful of seeds in each pot.