  We present on-sky polarimetric observations with the Gemini Planet Imager
(GPI) obtained at straight Cassegrain focus on the Gemini South 8-m telescope.
Observations of polarimetric calibrator stars, ranging from nearly unpolarized
to strongly polarized, enable determination of the combined telescope and
instrumental polarization. We find the conversion of Stokes $I$ to linear and
circular instrumental polarization in the instrument frame to be $I \rightarrow
(Q_{\rm IP}, U_{\rm IP}, P_{\rm IP}, V_{\rm IP}) = (-0.037 \pm 0.010\%, +0.4338
\pm 0.0075\%, 0.4354 \pm 0.0075\%, -6.64 \pm 0.56\%)$. Such precise measurement
of instrumental polarization enables $\sim 0.1\%$ absolute accuracy in
measurements of linear polarization, which together with GPI's high contrast
will allow GPI to explore scattered light from circumstellar disk in
unprecedented detail, conduct observations of a range of other astronomical
bodies, and potentially even study polarized thermal emission from young
exoplanets. Observations of unpolarized standard stars also let us quantify how
well GPI's differential polarimetry mode can suppress the stellar PSF halo. We
show that GPI polarimetry achieves cancellation of unpolarized starlight by
factors of 100-200, reaching the photon noise limit for sensitivity to
circumstellar scattered light for all but the smallest separations at which the
calibration for instrumental polarization currently sets the limit.
