We present the first detection of parallax effects in a gravitational microlensing event. Parallax in a gravitational microlensing event observed only from the Earth appears as a distortion of the lightcurve due to the motion of the Earth around the Sun. This distortion can be detected if the event duration is not much less than a year and if the projected velocity of the lens is not much larger than the orbital velocity of the Earth about the Sun. The event presented here has a duration of 220 days and clearly shows the distortion due to the Earths motion. We find that the projected velocity of the lens is 75+/-5 km/s at an angle of 28+/-4 deg from the direction of increasing galactic longitude, as expected for a lens in the galactic disk. A likelihood analysis yields estimates of the distance to and mass of the lens: D_{lens} = 1.7 (+1.1/-0.7) kpc and M = 1.3 (+1.3/-0.6) Msun, suggesting that the lens is a remnant such as a white dwarf or neutron star. A less likely possibility is that the lens is a main sequence star. If so, we can add our upper limit on the observed flux from the lens to the analysis. This modifies the estimates to: D_{lens} = 2.8 (+1.1/-0.6) kpc, and M = 0.6 (+0.4/-0.2) Msun.
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