Chester is a Pomeranian dog belonging to Chastity Claire Babcock played by Fran Drescher's own Pomeranian. Chester was bought for C.C. by Maxwell Sheffield because he was convinced that she was lonely. However, C.C. believed that Maxwell was going to propose to her, it also to an immediate disliking to C.C but it loved to be with Fran.
Chester was a birthday present for C.C from Maxwell.
A running gag in the show was the C.C. was constantly leaving Chester unattended (i.e. in a taxi, or in a duffel bag in her closet).
Another running gag is that Chester loathes C.C. almost as must as Niles does, but loves Fran very much.
In the episode Lamb Chop's on the Menu, Chester stays with the Sheffield's at Fran's suggestion because C.C. needed to get her apartment fumigated. At first, she was trying to find a kennel, but Fran suggested that Chester stay with them. During that time, however, Chester got ahold of Lamb Chop and, at first, it looked like Chester had eaten her. Later, it is revealed that he didn't eat her, but that he dumped her down the laundry chute. She is discovered on a towel at the end of the episode when Niles is folding the laundry.
Chester also stays with the Sheffield's after C.C. goes to rehab.