Actually, the answer is YES! Depending on the age of your chicks.
I know from personal experience that squirrels will attack and kill young chicks. The dirty little rodents did it to two of our nesting pairs of wild Blue birds just last summer. The parents haven't been back to those birdhouses since, despite four consecutive years of successful occupation by the same pairs.
And yes, we, my husband and me, both witnessed each of the events, so we know beyond a shadow of a doubt who did the evil deed!
Squirrels are cute and funny in their antics, but the truth be told, they're nothing more than disease carrying glorified rats! If I were you, I'd do everything I could short of killing them to keep them away from your chickens. Especially if they're very young! You might want to consider a live trap and transportation to a nice park miles away from your coop!
Please don't take this the wrong way....but have you ever seen what a weasel can do to full grown chickens? Squirrels are on a par with weasels when it comes to just how ferocious they can be. I'd just hate to see you go through the heartbreak of someday coming home to a coop of little lifeless bodies. Please think about my little nickels worth of free advice. At the very least, maybe hot wire their run to prevent entry by the squirrel.
I've never had a squirrel get after one of my birds though with young chicks I can certainly see that they might. I do have them get into my feeders often though where they can make a dang nuisance of themselves for the feed they eat or waste. Occasionally they'll also take eggs.