Ballooning modes are usually the most dangerous ideal MHD instabilities in stellarators, but the unstable ballooning modes often have such short perpendicular wavelengths that finite Larmor radius effects are sufficient to stabilize the plasma. We use semiclassical techniques to analyse this effect. In tokamaks the ignorable toroidal coordinate leads to a simple quantization of the ballooning mode, but this is not the case for stellarators. The ballooning mode dynamics in a stellarator model may possess a separation of timescales, in which case the system is integrable and quantization is straightforward, but we also present a method for determining marginal stability which is applicable to the non-integrable case.