Detecting polarized light from self-luminous exoplanets has the potential to provide key information about rotation, surface gravity, cloud grain size, and cloud coverage. While field brown dwarfs with detected polarized emission are common, no exoplanet or substellar companion has yet been detected in polarized light. With the advent of high contrast imaging spectro-polarimeters such as GPI and SPHERE, such a detection may now be possible with careful treatment of instrumental polarization. In this paper, we present 28 minutes of $H$-band GPI polarimetric observations of the benchmark T5.5 companion HD 19467 B. We detect no polarization signal from the target, and place an upper limit on the degree of linear polarization of $p_{text{CL}99.73%} leq 2.4%$. We discuss our results in the context of T dwarf cloud models and photometric variability.