How can I learn playing piano by ear?

I can do the right hand but not the left hand too well. Also timing is difficult for me when I try to put left and right together. Do I have to know chords to play? I know basic chords.

Hand coordination along with rhythm are some of the most common challenges for piano player. You can learn to play piano by sight reading or by improvising (play by ear). Below are some helpful websites:

http://www.yokewong.net

http://www.pianorhythm.com