We report the results from a new, highly sensitive ({Delta}T_mb_~3mK) survey for thermal OH emission at 1665 and 1667MHz over a dense, 9x9pix grid covering a 1{deg}x1{deg} patch of sky in the direction of l=105.00{deg}, b=+2.50{deg} toward the Perseus spiral arm of our Galaxy. We compare our Green Bank Telescope 1667MHz OH results with archival ^12^CO(1-0) observations from the Five College Radio Astronomy Observatory Outer Galaxy Survey within the velocity range of the Perseus Arm at these galactic coordinates. Out of the 81 statistically independent pointings in our survey area, 86% show detectable OH emission at 1667MHz, and 19% of them show detectable CO emission. We explore the possible physical conditions of the observed features using a set of diffuse molecular cloud models. In the context of these models, both OH and CO disappear at current sensitivity limits below an A_v_ of 0.2, but the CO emission does not appear until the volume density exceeds 100-200cm^-3^. These results demonstrate that a combination of low column density A_v_ and low volume density n_H_ can explain the lack of CO emission along sight lines exhibiting OH emission. The 18cm OH main lines, with their low critical density of n*~1cm^-3^, are collisionally excited over a large fraction of the quiescent galactic environment and, for observations of sufficient sensitivity, provide an optically thin radio tracer for diffuse H_2_.