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We report precise Doppler measurements of GJ317 (M3.5V) that reveal the presence of a planet with a minimum mass Msini = 1.2 Mjup in an eccentric, 692.9 day orbit. GJ317 is only the third M dwarf with a Doppler-detected Jovian planet. The residuals to a single-Keplerian fit show evidence of a possible second orbital companion. The inclusion of an additional Jupiter-mass planet (P = 2700 days, Msini = 0.83 Mjup) improves the quality of fit significantly, reducing the rms from 12.5 m/s to 6.32 m/s. A false-alarm test yields a 1.1% probability that the curvature in the residuals of the single-planet fit is due to random fluctuations, lending additional credibility to the two-planet model. However, our data only marginally constrain a two-planet fit and further monitoring is necessary to fully characterize the properties of the second planet. To study the effect of stellar mass on Jovian planet occurrence we combine our samples of M stars, Solar-mass dwarfs and intermediate-mass subgiants. We find a positive correlation between stellar mass and the occurrence rate of Jovian planets within 2.5 AU; the former A-type stars in our sample are nearly 5 times more likely than the M dwarfs to harbor a giant planet. Our analysis shows that the correlation between Jovian planet occurrence and stellar mass remains even after accounting for the effects of stellar metallicity.