We observed 51 Peg, the first detected planet-bearing star, in a 55 ks XMM-Newton pointing and in 5 ks pointings each with Chandra HRC-I and ACIS-S. The star has a very low count rate in the XMM observation, but is clearly visible in the Chandra images due to the detectors' different sensitivity at low X-ray energies. This allows a temperature estimate for 51 Peg's corona of T less than or similar to 1MK; the detected ACIS-S photons can be plausibly explained by emission lines of a very cool plasma near 200 eV. The constantly low X-ray surface flux and the flat-activity profile seen in optical Ca II data suggest that 51 Peg is a Maunder minimum star; an activity enhancement due to a Hot Jupiter, as proposed by recent studies, seems to be absent. The star's X-ray fluxes in different instruments are consistent with the exception of the HRC Imager, which might have a larger effective area below 200 eV than given in the calibration.