The Million-Grain Square

A ruler offers a clever scholar a reward measured out on a standard 64-square chessboard. One grain of wheat is placed on the first square. The second square receives two grains, the third receives four, and every later square receives twice as many grains as the square immediately before it. Ignore the running total across the board. Consider only the number of grains placed on each individual square. Which square is the first to receive more than one million grains?