A recycled juice bottle (single serving size) and have the toe of some pantyhose over it, which is fairly tight. I am keeping it inside my house, should I be chilling it? Does it overwinter like a mantis egg? Any idea when it will hatch? No other special care for it? Thanks so much!!

All the info I have for this species is on the guide page, which you can get to by clicking the gray "info" tab above. Apparently the adult will be fully developed by December. I assume that means it will chew its way out then, although it may be that it would overwinter in the gall before emerging. For galls that are meant to overwinter, it's important to keep them in an unheated place that gets natural light (such as by the window in a garage) so that the insect will experience both the temperatures and changing day lengths of winter. For this one, I'd say it's okay to keep it in your house, but if you haven't seen the adult by the end of December you might move it outside.

I will read up on the info tab. I'll keep it in the house for now and if nothing by December I'll find a place for it outside. I'll keep you updated!

To clarify-- "oak apple" is a general term for a number of different apple-like galls caused by different species of cynipid wasps. The gall John referenced above is a spring gall (see BugGuide data), so I don't think this is that one. This may be the gall pictured below, which forms on the fall on post oak leaves. Confirming the species of oak, as John mentioned, would be very helpful.

Go out and get a full leaf from that same area and add a picture on to here tomorrow. Thank you both!