We report on a deep search with the Westerbork Synthesis Radio Telesco
pe towards the galactic anticenter for the 327 MHz hyperfine transitio
n of DI. This is a favorable direction for a search because: (i) the H
I optical depth is high due to velocity crowding; (ii) the observed mo
lecular column density is low (implying that most of the deuterium wou
ld probably be in atomic form, rather than in HD); and (iii) the stell
ar reprocessing should be minimal. Our observations are about a factor
of two more sensitive than previous searches for DI in this direction
. We detect a low significance (similar to 4 sigma) feature, consisten
t in both amplitude and center frequency with an emission feature repo
rted previously (Blitz & Heiles 1987). If this is the DI line, then th
e implied N-D/N-H of 3.9 +/- 1.0 X 10(-5) is comparable to the inferre
d pre-solar deuterium abundance. Our observation is consistent with th
e recent low measurements of D/H towards high-redshift Lyman-limit sys
tems. On the other hand, if the reports of high DI abundance (similar
to 24 X 10(-5)) in such systems are confirmed, then our observations i
mply that even in regions of reduced star formation within the outer G
alaxy, the DI abundance has been reduced by a factor of similar to 6 f
rom the primordial abundance.