We report the results from a new, highly sensitive (∆T mb ∼ 3mK) survey for thermal OH emission at 1665 and 1667 MHz over a dense, 9 x 9-pixel grid covering a 1 • × 1 • patch of sky in the direction of l = 105. • 00, b = +2. • 50 towards the Perseus spiral arm of our Galaxy. We compare our Green Bank Telescope (GBT) 1667 MHz OH results with archival 12 CO(1-0) observations from the Five College Radio Astronomy Observatory (FCRAO) 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 1667 MHz, 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 100-200 cm −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 18-cm OH main lines, with their low critical density of n * ∼ 1 cm −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 .