We report the results of deep observations at radio (3.6 cm) wavelengths of the nearby solar-type star &pgr;01 Ursa Majoris with the Very Large Array (VLA) intended to test an alternative theory of solar luminosity evolution. The standard model predicts a solar luminosity only 75% of the present value and surface temperatures below freezing on Earth and Mars at 4 Ga, seemingly in conflict with geologic evidence for liquid water on these planets. An alternative model invokes a compensatory mass loss through a declining solar wind that results in a more consistent early luminosity. The free-free emission from an enhanced wind around nearby young Sun-like stars should be detectable at microwave frequencies. Our observations of &pgr;01 UMa, a 300 million year-old solar-mass star, place an upper limit on the mass loss rate of 4-5¿10-11 M⊙ yr-1. Total mass loss from such a star over 4 Gyr would be less than 6%. If this star is indeed an analog of the early Sun, it casts doubt on the alternative model as a solution to the faint young Sun paradox, particularly for Mars. ¿ 2000 American Geophysical Union