Serendipitous Detection of HI Absorption Sets the True Redshift of 4C +15.05 to $z=0.833$.

4C+15.05, (also known as NRAO 91, PKS 0202+14 or J0204+15), is a quintessential blazar. It has a luminous, variable radio spectrum, a super-luminal jet, and gamma-ray detections. Arecibo observations with the 700-800 MHz receiver on the 305-m diameter William E. Gordon Telescope detected, serendipitously, HI in absorption against 4C+15.05 while using it as a bandpass calibrator for another object in an HI absorption project. Although the redshift we derive is different from that commonly in use in the literature (nominally $z=0.405$), it agrees very well with the value of $z=0.833$ determined by \cite{Stickel+96}. This absorption feature is best fitted by a sum of three Gaussians, which yield an average redshift of $z=0.8336 \pm 0.0004$, although without corresponding high resolution imaging it is not possible to say whether the components are parts of outflows or inflows. A total column density of $N(HI) = 2.39 \pm 0.13 \times 10^{21}$ cm$^{-2}$ is derived, relatively high compared to many radio-loud sources. These results are compared to various relationships in the literature.