The relatively nearby (distance = 24.1 Mpc) elliptical galaxy NGC 821, hosting a central massive black hole but inactive at all wavelengths, was observed with Chandra for a total exposure time of 230 ks in order to search for nuclear emission and gas available for accretion. Within its optical image, 41 sources were detected, with spectral properties typical of low-mass X-ray binaries (LMXBs). The fractions of LMXBs in the field and in globular clusters were determined, together with their X-ray luminosity function (XLF), down to L(0.3-8 keV) = 2 × 1037 ergs s-1. At the galactic center a source of L(0.3-8 keV) = 6 × 1038 ergs s-1 was detected for the first time, slightly extended. Its spectral shape is quite hard (Γ = 1.49), without intrinsic absorption. It is surrounded by three sources with spectral shapes typical of LMXBs and luminosities on the brightest end of the XLF. One is consistent with being pointlike; the others could be the superposition of a few point sources and/or truly diffuse emission, with one resembling a jetlike feature. Diffuse emission was detected out to R ~ 30'' and comes mostly from unresolved LMXBs, with a minor contribution from other types of stellar sources. Different lines of investigation consistently provide no evidence for hot gas. Hydrodynamical simulations show that stellar mass losses are driven out of NGC 821 in a wind sustained by Type Ia supernovae, but also hot accreting gas within a very small inner region. A companion paper presents further observational results from Spitzer and the Very Large Array (VLA), and possible accretion modalities for this central massive black hole.