Forecasting the intensity of tropical cyclones is a challenging problem. Rapid intensification is often preceded by the formation of "hot towers near the eyewall. Driven by strong release of latent heat, hot towers are high-reaching tropical cumulonimbus clouds that penetrate the tropopause. Hot towers are a potentially important source of stratospheric gravity waves. Using 13.5 years (2002-2016) of Atmospheric Infrared Sounder observations of stratospheric gravity waves and tropical cyclone data from the International Best Track Archive for Climate Stewardship, we found empirical evidence that stratospheric gravity wave activity is associated with the intensification of tropical cyclones. The Atmospheric Infrared Sounder and International Best Track Archive for Climate Stewardship data showed that strong gravity wave events occurred about twice as often for tropical cyclone intensification compared to storm weakening. Observations of stratospheric gravity waves, which are not affected by obscuring tropospheric clouds, may become an important future indicator of storm intensification.