We present observations of microlensing event MACHO-98-BLG-35 which reached a peak magnification factor of almost 80. These observations by the Microlensing Planet Search (MPS) and the MOA Collaborations place strong constraints on the possible planetary system of the lens star and show intriguing evidence for a low mass planet with a mass fraction $4times 10^{-5} leq epsilon leq 2times 10^{-4}$. A giant planet with $epsilon = 10^{-3}$ is excluded from 95% of the region between 0.4 and 2.5 $R_E$ from the lens star, where $R_E$ is the Einstein ring radius of the lens. This exclusion region is more extensive than the generic lensing zone which is $0.6 - 1.6 R_E$. For smaller mass planets, we can exclude 57% of the lensing zone for $epsilon = 10^{-4}$ and 14% of the lensing zone for $epsilon = 10^{-5}$. The mass fraction $epsilon = 10^{-5}$ corresponds to an Earth mass planet for a lensing star of mass $sim 0.3 msun$. A number of similar events will provide statistically significant constraints on the prevalence of Earth mass planets. In order to put our limits in more familiar terms, we have compared our results to those expected for a Solar System clone averaging over possible lens system distances and orientations. We find that such a system is ruled out at the 90% confidence level. A copy of the Solar System with Jupiter replaced by a second Saturn mass planet can be ruled out at 70% confidence. Our low mass planetary signal (few Earth masses to Neptune mass) is significant at the $4.5sigma$ confidence level. If this planetary interpretation is correct, the MACHO-98-BLG-35 lens system constitutes the first detection of a low mass planet orbiting an ordinary star without gas giant planets.
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