Kolya's attempt to get Vadim out of the coop and into the care of the girls again indicates that for all Kolya's posturing and swagger, he really is a caring person. When Vadim gives Kolya the chicken, the boy surrenders to his own death. It's indicated that he's not going to live even though Kolya leaves him with food and money, making Kolya’s gift of food a symbolic gesture and nothing more. And yet, in a besieged city where people are buying jars of dirt for food, that is a pretty profound symbolic gesture. Kolya is willing to sacrifice his own comfort in exchange for the comfort of a dying boy.