  We report the results of a new 60 ks Chandra X-ray Observatory Advanced CCD
Imaging Spectrometer S-array (ACIS-S) observation of the reddened,
radio-selected, highly polarized `FeLoBAL' quasar FIRST J1556+3517. We
investigated a number of models of varied sophistication to fit the 531-photon
spectrum. These models ranged from simple power laws to power laws absorbed by
hydrogen gas in differing ionization states and degrees of partial covering.
Preferred fits indicate that the intrinsic X-ray flux is consistent with that
expected for quasars of similarly high luminosity, i.e., an intrinsic,
dereddened and unabsorbed optical to X-ray spectral index of -1.7. We cannot
tightly constrain the intrinsic X-ray power-law slope, but find indications
that it is flat (photon index Gamma = 1.7 or flatter at a >99% confidence for a
neutral hydrogen absorber model). Absorption is present, with a column density
a few times 10^23 cm^-2, with both partially ionized models and partially
covering neutral hydrogen models providing good fits. We present several lines
of argument that suggest the fraction of X-ray emissions associated with the
radio jet is not large.
  We combine our Chandra data with observations from the literature to
construct the spectral energy distribution of FIRST J1556+3517 from radio to
X-ray energies. We make corrections for Doppler beaming for the pole-on radio
jet, optical dust reddening, and X-ray absorption, in order to recover a
probable intrinsic spectrum. The quasar FIRST J1556+3517 seems to be an
intrinsically normal radio-quiet quasar with a reddened optical/UV spectrum, a
Doppler-boosted but intrinsically weak radio jet, and an X-ray absorber not
dissimilar from that of other broad absorption line quasars.
