  We report on the quiescent spectrum measured with Chandra/ACIS-S of the
transient, type-I X-ray bursting neutron star Aql X-1, immediately following an
accretion outburst. The neutron star radius, assuming a pure hydrogen
atmosphere and hard power-law spectrum, is $R_\infty$=13.4{+5}{-4} (d/5 \kpc)
km. Based on the historical outburst record of RXTE/ASM, the quiescent
luminosity is consistent with that predicted by Brown, Bildsten and Rutledge
from deep crustal heating, lending support to this theory for providing a
minimum quiescent luminosity of transient neutron stars. While not required by
the data, the hard power-law component can account for 18+/-8% of the 0.5-10
keV thermal flux. Short-timescale intensity variability during this observation
is less than 15% rms (3 sigma; 0.0001-1 Hz, 0.2-8 keV). Comparison between the
Chandra spectrum and three X-ray spectral observations made between Oct 1992
and Oct 1996 find all spectra consistent with a pure H atmosphere, but with
temperatures ranging from 145--168 eV, spanning a factor of 1.87+/-0.21 in
observed flux. The source of variability in the quiescent luminosity on long
timescales (greater than years) remains a puzzle. If from accretion, then it
remains to be explained why the quiescent accretion rate provides a luminosity
so nearly equal to that from deep crustal heating.
