  We present a Chandra ACIS-S observation of the nearby bulge-dominated Sa
galaxy NGC1291. The X-ray emission from the bulge resembles the X-ray emission
from a sub-class of elliptical and S0 galaxies with low L_X/L_B luminosity
ratios. The X-ray emission is composed of a central point-like nucleus, ~50
point sources that are most likely low mass X-ray binaries (LMXBs), and diffuse
gas detectable out to a radius of 120" (5.2 kpc). The diffuse gas has a global
temperature of 0.32^{+0.04}_{-0.03} keV and metallicity of 0.06 +/- 0.02 solar,
and both quantities marginally decrease with increasing radius. The hot gas
fills the hole in the HI distribution, and the softening of the spectrum of the
X-ray gas with radius might indicate a thermal coupling of the hot and cold
phases of the interstellar medium as previously suggested. The integrated X-ray
luminosity of the LMXBs, once normalized by the optical luminosity, is a factor
of 1.4 less than in the elliptical galaxy NGC4697 or S0 galaxy NGC1553. The
difference in L_{X,stellar}/L_B between the galaxies appears to be because of a
lack of very bright sources in NGC1291. No sources above 3 x 10^38 ergs/s were
found in NGC1291 when ~7 were expected from scaling from NGC4697 and NGC1553.
The cumulative L_{X,stellar}/L_B value including only sources below 1.0 x 10^38
ergs/s is remarkably similar between NGC1291 and NGC4697, if a recent surface
brightness fluctuation-determined distance is assumed for NGC4697. If this is a
common feature of the LMXB population in early-type systems, it might be used
as a distance indicator. Finally, a bright, variable (1.6-3.1 x 10^39 ergs/s)
source was detected at the optical center of the galaxy. Its spectrum shows
excess soft emission superimposed on a highly absorbed power law component,
similar to what has been found in several other low luminosity AGN (ABRIDGED).
