In this paper we report the first measurements of the thermosphere neutral density response to a solar EUV flare. Two X17 flares are considered: The first on 28 October, 2003, and the second on 4 November, 2003. The density measurements are provided by accelerometers on the GRACE and CHAMP satellites near 490 km and 400 km, respectively. X-ray fluxes are provided by GOES-12, and EUV fluxes by the SEE instrument on TIMED. The thermosphere density increases associated with the first flare are about 50--60% at low to mid-latitudes. The time to peak response is 72 ¿ 47 minutes with respect to the peak EUV flux emitted by the flare, while the recovery to prior quiescent levels takes nearly 12 hours with an approximate decay time constant of 8 hours. The response to the second flare is about 35--45% with similar response and recovery times. The above density enhancements correspond to exosphere temperature increases of about 125--175 K and 100--125 K, respectively. These results provide new opportunities for the testing and validation of models over time scales similar to those of basic mechanisms governing the thermosphere response, such as thermal conduction, radiative cooling, and restoration of diffusive equilibrium.