We search for signatures of planets in 43 intensively monitored microlensing events that were observed between 1995 and 1999. Planets would be expected to cause a short duration (~1 day) deviation on the smooth, symmetric light curve produced by a single-lens. We find no such anomalies and infer that less than 1/3 of the ~0.3 M_sun stars that typically comprise the lens population have Jupiter-mass companions with semi-major axes in the range of 1.5 AU <a < 4 AU. Since orbital periods of planets at these radii are 3-15 years, the outer portion of this region is currently difficult to probe with any other technique.
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