Patriotic chameleons

This is a problem I saw on someone's Putnam Exam review sheet.

Puzzle

For last year's 4th of July party, you bought 2010 chameleons: an equal number colored red, white, and blue. These chameleons have the strange property that whenever two of different colors meet, they both change into the third color. After the party, you worry that while in storage for next year's party, the chameleons will all change into a single color, thus making it impossible to recreate the patriotic mix of colors. To remedy this problem, you go ahead an buy one more chameleon. Will the 2011 chameleons ever be all the same color?