  The sterile neutrino is a weakly-interacting particle that emerges in the
framework of certain extensions of standard particle physics and that fits
naturally with the properties of a warm dark matter particle candidate. We
present an analysis of a deep archival Chandra observation of Willman 1, one of
the darkest purported ultra-faint dwarf galaxies, that excludes the presence of
sterile neutrinos in the 1.6-16 keV mass range within 55 pc of its centre down
to the limits of the observation. Spectral analysis of the Chandra data fails
to find any non-instrumental spectral feature possibly connected with the
radiative decay of a dark matter particle. Accordingly, we establish upper
bounds on the sterile neutrino parameter space and discuss it in the context of
previous measurements. Regarding the point source population, we identify a
total of 26 sources within the central 5 arcminutes to a limiting 0.5-2.0 keV
X-ray flux of 6 x 10^{-16} erg cm^{-2} s^{-1}. While some of these sources
could be formal members of Willman 1, we find no outstanding evidence for
either an unusual population of bright X-ray sources or a densely populated
cluster core. In fact, the entire X-ray population could be explained by
background active galactic nuclei and/or foreground stars unrelated to Willman
1. Finally, possible associations of the X-ray point like population with
optical sources from the SDSS DR7 catalogue are discussed.
