What kind of damage do you deal when successfully defending with Chalk?
You will still inflict or take physical damage.

The rule that allows you to deal mental damage with attacking refers specifically to attacking with that trait, not defending with that trait:


  When a card or a haunt lets you attack with Sanity or Knowledge, then you inflict mental damage. You and your opponent move down your Sanity and/or Knowledge traits. 


Also note that if the monster doesn't have a knowledge trait (which most do not), then you cannot inflict knowledge damage in the first place:


  You can’t use a trait to attack an opponent who doesn’t have that trait. For instance, if a monster doesn’t have Sanity, you can’t make a Sanity attack against it.


So if Chalk did allow you to deal damage as if it were mental; you wouldn't be allowed to use it against most monsters. However, Chalk simply changes the way you defend; it is still a normal might-based combat.

Finally, note the wording on the item Ring:


  [...] (Your opponent then defends with Sanity, and damage is mental instead of physical.)


Ring calls out specifically that damage is mental; while Chalk does not.