This is an interesting question.

First of all, your **human body is not a rigid system**. So basically while you are attempting to do this act, you can observe that different portions of your body move in different directions or creating a small wave. While trying to move the chair forward, your upper body moves forward then the pulls your lower  body towards it, now, the real question is *where does the upper body get that support from to pull the lower body?* 

Here comes **inertia** into play. When you jerk your upper body, *it resists moving till a certain amount of time*, this is inertia's role. So what you are basically doing is you are by jerking your body in that fashion, you are harvesting the force of inertia and use that to move the chair. This resistance exist's only till a limited amount of time or till your body is trying to accelerate itself because that is inertia's nature. Try to move a longer distance in a single wave, tat might help you getting a better perception of it.

Hope that helps.