Strengthen your obliques to do more pull-ups and chin-ups

Chin-ups and Pull-ups.  If you're looking to increase the number of pull-ups or pull-ups in your routine, try exercising the obliques and your lats.  

from Livestrong,

Your latissimus dorsi is the most powerful pulling muscle in your back, and during a pull-up, it's the primary mover or the muscle that provides most of the power to bring your body up to the bar. One of the movements it performs is shoulder adduction, or bringing your arms down toward the sides of your body. But because the pull-up bar is fixed in place and your body is not, it's your body that moves up to the bar.

The latissimus dorsi, commonly referred to as the lats,

Strengthen your obliques like this,

and this,

So that you can do more of these,