  We report on Chandra X-ray Observatory (CXO) High-Energy Transmission Grating
(HETG) spectra of the dipping Low Mass X-ray Binary (LMXB) 1A 1744-361 during
its July 2008 outburst. We find that its persistent emission is well modeled by
a blackbody (kT ~ 1.0 keV) plus power-law ($\Gamma$ ~ 1.7) with an absorption
edge at 7.6 keV. In the residuals of the combined spectrum we find a
significant absorption line at 6.961+/-0.002 keV, consistent with the Fe XXVI
(hydrogen-like Fe) 2 - 1 transition. We place an upper limit on the velocity of
a redshifted flow of v < 221 km/s. We find an equivalent width for the line of
27^+2_-3 eV, from which we determine a column density of 7+/-1x10^17 cm^-2 via
a curve-of-growth analysis. Using XSTAR simulations, we place a lower limit on
the ionization parameter of > 10^3.6 erg cm/s. The properties of this line are
consistent with those observed in other dipping LMXBs. Using Rossi X-ray Timing
Explorer (RXTE) data accumulated during this latest outburst we present an
updated color-color diagram which clearly shows that 1A 1744-361 is an "atoll"
source. Finally, using additional dips found in the RXTE and CXO data we
provide an updated orbital period estimate of 52+/-5 minutes.
