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The hydroxyl radical (OH) is present in the diffuse molecular and partiallyatomic phases of the interstellar medium (ISM), but its abundance relative tohydrogen is not clear. We aim to evaluate the abundance of OH with respect tomolecular hydrogen using OH absorption against cm-continuum sources over thefirst Galactic quadrant. This OH study is part of the HI/OH/Recombination linesurvey (THOR). THOR is a Karl G. Jansky Very Large Array large program ofatomic, molecular and ionized gas in the range 15{\deg}$\leq$l$\leq$67{\deg}and |b|$\leq$1{\deg}. It is the highest-resolution unbiased OH absorptionsurvey to date towards this region. We combine the derived optical depths withliterature 13CO(1-0) and HI observations to determine the OH abundance. Wedetect absorption in the 1665 and 1667 MHz transitions for continuum sourcesstronger than $F_{\rm cont}\geq$0.1 Jy/beam. OH absorption is found against$\sim$15% of these continuum sources with increasing fractions for strongersources. Most of the absorption is associated with Galactic HII regions. Wefind OH and 13CO gas to have similar kinematic properties. The OH abundancedecreases with increasing hydrogen column density. The OH abundance withrespect to the total hydrogen nuclei column density (atomic and molecularphase) is in agreement with a constant abundance for $A_V$ < 10-20. Towards thelowest column densities, we find sources that exhibit OH absorption but no 13COemission, indicating that OH is a well suited tracer of the low column densitymolecular gas. We present spatially resolved OH absorption towards W43. Theunbiased nature of the THOR survey opens a new window onto the gas propertiesof the ISM. The characterization of the OH abundance over a large range ofhydrogen gas column densities contributes to the understanding of OH as amolecular gas tracer and provides a starting point for future investigations.

OH absorption in the first quadrant of the Milky Way as seen by THOR