Recently, Knutson et al. have demonstrated a correlation between the presence of temperature inversions in the atmospheres of hot Jupiters and the chromospheric activity levels of the host stars. Here, we show that there is also a correlation, with greater than 99.5% confidence, between the surface gravity of hot Jupiters and the activity levels of the host stars, such that high surface gravity planets tend be found around high-activity stars. We also find a less significant positive correlation between planet mass and chromospheric activity, but no significant correlation is seen between planet radius and chromospheric activity. We consider the possibility that this may be due to an observational bias against detecting lower mass planets around higher activity stars, but conclude that this bias is only likely to affect the detection of planets much smaller than those considered here. Finally, we speculate on physical origins for the correlation—including the possibility that the effect of stellar insolation on planetary radii has been significantly underestimated, that strong UV flux evaporates planetary atmospheres, or that high-mass hot Jupiters induce activity in their host stars—but do not find any of these hypotheses to be particularly compelling.