Observations of the gravitational microlensing event MOA 2003-BLG-32/OGLE 2003-BLG-219 are presented, for which the peak magnification was over 500, the highest yet reported. Continuous observations around the peak enabled a sensitive search for planets orbiting the lens star. No planets were detected. Planets 1.3 times heavier than Earth were excluded from more than 50% of the projected annular region from approximately 2.3 to 3.6 astronomical units surrounding the lens star, Uranus-mass planets were excluded from 0.9 to 8.7 astronomical units, and planets 1.3 times heavier than Saturn were excluded from 0.2 to 60 astronomical units. These are the largest regions of sensitivity yet achieved in searches for extrasolar planets orbiting any star.