Monkey is the dog Dan gave Chuck as another way to relieve his psychological pain from losing Blair. During Chuck's "path to being good" in Season 5 Monkey is seen most often in Chuck's Hotel Empire penthouse and walking with Chuck in Central Park.
Chuck first refers to monkey as a mutt but grows to love him. Blair got angry at Chuck when she saw a Gossip Girl blast of him giving the dog away but later we find out Chuck got monkey neutered. Monkey and Chuck seem to have the closest relationship with one and other. Monkey is very friendly towards Dan and Nate. He can be very vicious at the command of Chuck.