Can you put a T-Mobile SIM card into a Unlocked At&T pre-paid phone?

I don't talk on the phone much so I am thinking about getting a pre paid At&t phone off of Ebay. I already had a T-mobile pre paid phone but it is tearing up and hardly picks up anywhere. The phone I am getting is Unlocked already and I was wondering if I can take my chip out of my T-mobile and put it in the new phone that I am getting.

By the way I'm getting this phone:

Samsung SGH a187 :)
 
Top