What guitar chord is this?

Chords are constructed (and named) according to formulas derived from scales. Since all scales are based on the same 12 notes, you can run into situations where two different chords can share the same notes. In this case, it's C6 or Am7, depending on the context. You can check it here: http://www.all-guitar-chords.com/chord_name.php

or A minor 7 (Am7). Can be played when music calls for A minor.

Am7/G