Chomp on a 2x3 Bar

Chomp is played on a 2-by-3 grid of chocolate squares; the top-left square (row 1, column 1) is poisoned. A move picks any remaining square and eats it together with every square below and to the right of it. The player forced to eat the poisoned top-left square loses. Under optimal play, does the first player win or lose, and what is the standard argument?