  We have observed Proxima Centauri and Barnard's Star with Hubble Space
Telescope Fine Guidance Sensor 3. Proxima Centauri exhibits small-amplitude,
periodic photometric variations. Once several sources of systematic photometric
error are corrected, we obtain 2 milli-magnitude internal photometric
precision. We identify two distinct behavior modes over the past four years:
higher amplitude, longer period; smaller amplitude, shorter period. Within the
errors one period (P ~ 83d) is twice the other. Barnard's Star shows very weak
evidence for periodicity on a timescale of approximately 130 days. If we
interpret these periodic phenomena as rotational modulation of star spots, we
identify three discrete spots on Proxima Cen and possibly one spot on Barnard's
Star. We find that the disturbances change significantly on time scales as
short as one rotation period.
