Pure css Chessboard with div & no classes or ids, is it possible?

This is an interesting problem. I think a chess board is better expressed as a table than as a series of divs, as a screen reader would dictate the rows and columns where the figures are located. With a table:

table tr:nth-child(odd) td:nth-child(even) {
  background: #000;
}
table tr:nth-child(even) td:nth-child(odd) {
  background: #000;
}

http://jsfiddle.net/9kWJZ/

You don't have to hardcode each :nth-child(). Here's one way to shorten it. Each selector corresponds to a row on the chessboard:

#chess div:nth-child(-2n+8), 
#chess div:nth-child(8) ~ div:nth-child(-2n+15), 
#chess div:nth-child(16) ~ div:nth-child(-2n+24),
#chess div:nth-child(24) ~ div:nth-child(-2n+31),
#chess div:nth-child(32) ~ div:nth-child(-2n+40),
#chess div:nth-child(40) ~ div:nth-child(-2n+47),
#chess div:nth-child(48) ~ div:nth-child(-2n+56),
#chess div:nth-child(56) ~ div:nth-child(-2n+63) {
    background-color: #000;
}

jsFiddle preview