Most of the time chords are played with your left hand, while the melody (the tune of the song) is played with the right hand. But it is also possible to play chords with the right hand and not play any in the left. Watch me illustrate this on the video:

Of course, the best way is to use chords in both hands. That way you get a much fuller sound.

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http://www.youtube.com/watch?v=EdPSJ-Fosgw&feature=youtu.be