Doing exercises on the ball, can increase core stability.  Doing the chest press on the ball increases your core stability, shoulder stability, and hip stability.
 
To further increase the challenge to your stability you can do the alternating chest press or the 1 arm chest press.
 

The 1 arm chest flye on a flat bench is one of the hardest chest exercises on core stability.  When you only use one dumbbell at a time there is no counter balance.   So, your core muscles must work to keep your body stable.
 

Alternating chest flyes are a great way to work your chest muscles and your core muscles at the same time.
 
You can do alternating flyes on a decline bench, flat bench, or incline bench to emphasize the chest a little differently each time.
 

Learn the best chest exercises and picutures of the best arm exercises at http://www.All-About-Arm-Exercises.com
 
In addition to all the best chest exercises, learn the best back exercises and rotator cuff exercises, and get upper body workout tips.

Hey Everyone,
 
I been working on a new website for quite a while now, and I still want to do a lot more to improve it.  But I figured I'd share it with you and hope that you'll find some useful information on it.
 
The site is called All-About-Arm-Exercises.com and it has pictures of bicep exercises, tricep exercises, back exercises, chest exercises, rotator cuff exercises, and shoulder exercises.  It also has a few free arm workouts and tips about weight lifting.