  We have analyzed Chandra calibration observations of Betelgeuse (alpha Ori,
M2Iab, m_V=0.58, 131 pc) obtained at the aimpoint locations of the HRC-I (8
ks), HRC-S (8 ks), and ACIS-I (5 ks). Betelgeuse is undetected in all the
individual observations as well as cumulatively. We derive upper limits to the
X-ray count rates and compute the corresponding X-ray flux and luminosity upper
limits for coronal plasma that may potentially exist in the atmosphere of
Betelgeuse over a range of temperatures, T=0.3-10 MK. We place a flux limit at
the telescope of fx ~ 4x10^(-15) ergs s^(-1) cm^(-2) at T=1 MK. The upper limit
is lowered by a factor of ~3 at higher temperatures, roughly an order of
magnitude lower than that obtained previously. Assuming that the entire stellar
surface is active, these fluxes correspond to a surface flux limit that ranges
from 30-7000 ergs s^(-1) cm^(-2) at T=1 MK, to ~1 ergs s^(-1) cm^(-2) at higher
temperatures, five orders of magnitude below the quiet Sun X-ray surface flux.
We discuss the implications of our analysis in the context of models of a
buried corona and a pervasive magnetic carpet. We rule out the existence of a
solar-like corona on Betelgeuse, but cannot rule out the presence of low-level
emission on the scale of coronal holes.
