On-Site Inspection (OSI) is a key component of the verification regime for the Comprehensive Nuclear-Test-Ban Treaty (CTBT). Measurements of radionuclide isotopes created by an underground nuclear explosion are a valuable signature of a Treaty violation. Argon-37 is produced from neutron interaction with calcium in soil, 40Ca(n,{\alpha})37Ar. For OSI, the 35-day half-life of 37Ar provides both high specific activity and sufficient time for completion of an inspection before decay limits sensitivity. This paper presents a low-background internal-source gas proportional counter with an 37Ar measurement sensitivity level equivalent to 45.1 mBq/SCM in whole air.