Chandra has detected optically-thin, thermal X-ray emission with a size of ∼1 arcsec and luminosity ∼1033 erg s−1 from the direction of the Galactic supermassive black hole (SMBH), Sgr A*. We suggest that a significant or even dominant fraction of this signal may be produced by several thousand late-type main-sequence stars that possibly hide in the central ∼0.1 pc region of the Galaxy. As a result of tidal spin-ups caused by close encounters with other stars and stellar remnants, these stars should be rapidly rotating and hence have hot coronae, emitting copious amounts of X-ray emission with temperatures kT≲ a few keV. The Chandra data thus place an interesting upper limit on the space density of (currently unobservable) low-mass main-sequence stars near Sgr A*. This bound is close to and consistent with current constraints on the central stellar cusp provided by infrared observations. If coronally active stars do provide a significant fraction of the X-ray luminosity of Sgr A*, then it should be moderately variable on hourly and daily time-scales due to giant flares occurring on different stars. Another consequence is that the quiescent X-ray luminosity and accretion rate of the SMBH are yet lower than believed before.