What little I know of music theory appears to not be enough for me to put a name to a chord I have used from time to time. The chord charts I've consulted are of no help. Perhaps one of you can figure out what it should be called and give your logic for doing so.

On the guitar it looks in shape like an E chord that has slipped over one string and down one fret. Thus, we have the middle finger on 6th string 3rd fret, ring finger on 5th string 3rd fret and index finger on 4th string 2nd fret. All other strings are open. This would make it from 6th to 1st: G, C, E, G, B, E. Any ideas?