Long-term thermospheric neutral density trends near 400 km altitude are analyzed using high accuracy satellite drag measurements over the common time period 1970--2000. Data coverage is over all latitudes and local times and an extensive range of solar and geomagnetic conditions. Densities are compared to empirical models that remove known variations related to solar activity, latitude, local time, day of year and altitude. An average unmodeled secular neutral density decrease of 1.7% per decade is detected. This result is qualitatively consistent with predictions of thermospheric cooling related to anthropogenic causes deduced by theoretical models, and in general agreement with global cooling estimates determined from previous analyses of satellite orbital decay.