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 4 \times 10 ^ { -5 } \leq \epsilon \leq 2 \times 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 { M _ { \odot } } . 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 4.5 \sigma 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 . The data are available for interested readers in the following web sites . MPS http : //bustard.phys.nd.edu/MPS/98-BLG-35 MOA http : //www.phys.vuw.ac.nz/dept/projects/moa/9835/9835.html