We report millimeter observations of the line of sight to the recently discovered Soft Gamma Repeater, SGR 1627-41, which has been tentatively associated with the supernova remnant SNR G337.0-0.1 Among the eight molecular clouds along the line of sight to SGR 1627-41, we show that SNR G337.0-0.1 is probably interacting with one of the most massive giant molecular clouds (GMC) in the Galaxy, at a distance of 11 kpc from the sun. Based on the high extinction to the persistent X-ray counterpart of SGR 1627-41, we present evidence for an association of this new SGR with the SNR G337.0-0.1; they both appear to be located on the near side of the GMC. This is the second SGR located near an extraordinarily massive GMC. We suggest that SGR 1627-41 is a neutron star with a high transverse velocity (~ 1,000 kms) escaping the young (~ 5,000 years) supernova remnant G337.0-0.1
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