The chainsaw's V.A.T.S. attack animation is unusual due to the automatic nature of the weapon type. The attack is initiated but the automatic damage is not applied, nor does the target act as if harmed, until the end of the attack when the damage is finally applied. It also has a slight knockback effect.
The chainsaw, along with the Ripper, is one of two weapons in Fallout: New Vegas that non-player characters use differently than the player character. Rather than using the thrust attack, they use the V.A.T.S.-style slash. This can cause a large amount of damage.