We report millimeter observations of the line of sight to the recently disc
overed soft gamma repeater SGR 1627-41, which has been tentatively associat
ed with the supernova remnant (SNR) G337.0-0.1. Among the eight molecular c
louds along the line of sight to SGR 1627-41, we show that SNR G337.0-0.1 i
s probably interacting with one of the most massive giant molecular clouds
(GMCs) in the Galaxy, at a distance of 11 kpc from the Sun. Based on the hi
gh extinction to the persistent X-ray counterpart of SGR 1627-41, we presen
t evidence for an association of this new soft gamma repeater (SGR) with th
e SNR G337.0-0.1; they both appear to be located on the near side of the GM
C. This is the second SGR located near an extraordinarily massive GMC. We s
uggest that SGR 1627-41 is a neutron star with a high transverse velocity (
similar to 1000 km s(-1)) escaping the young (similar to 5000 yr) SNR G337.
0-0.1.