When you move a chair across the floor, the main force you must overcome with your push is the frictional force between the chair’s legs and the floor. Friction acts parallel to the surface of contact and opposite to the direction of motion or relative motion. Initially, when the chair is at rest, static friction acts to resist the start of movement. Once the chair is in motion, kinetic friction continues to oppose the movement, requiring you to apply a force stronger than this frictional force to keep the chair moving across the floor.

In summary, your push must exceed the force of friction in order to successfully move the chair across the floor.