You must first understand what you are trying to accomplish when voicing your chord and think of your hands as a team trying to obtain a common goal. For example, a C chord consist of the notes C, E, G. Somehow divide this chord between your two hands. (foot: C left hand: E G Right Hand: E G C )
In addition, when an experienced musician realizes that they have to play a C chord, they have a bank of options in which to pull from that has been collected over their musical careers.
Also, do not feel obligated to play with your left hand all the time. When I first started playing, I was infatuated with runs. Then it was the left hand chording. Now I appreciate the little things in music such as dynamics, rhythm, note values, and chord placements. Always play what is needed to make a song effective.