  We measure weak lensing cosmic shear power spectra from the three-year galaxy
shear catalog of the Hyper Suprime-Cam (HSC) Subaru Strategic Program imaging
survey. The shear catalog covers $416 \ \mathrm{deg}^2$ of the northern sky,
with a mean $i$-band seeing of 0.59 arcsec and an effective galaxy number
density of 15 $\mathrm{arcmin}^{-2}$ within our adopted redshift range. With an
$i$-band magnitude limit of 24.5 mag, and four tomographic redshift bins
spanning $0.3 \leq z_{\mathrm{ph}} \leq 1.5$ based on photometric redshifts, we
obtain a high-significance measurement of the cosmic shear power spectra, with
a signal-to-noise ratio of approximately 26.4 in the multipole range
$300<\ell<1800$. The accuracy of our power spectrum measurement is tested
against realistic mock shear catalogs, and we use these catalogs to get a
reliable measurement of the covariance of the power spectrum measurements. We
use a robust blinding procedure to avoid confirmation bias, and model various
uncertainties and sources of bias in our analysis, including point spread
function systematics, redshift distribution uncertainties, the intrinsic
alignment of galaxies and the modeling of the matter power spectrum. For a flat
$\Lambda$CDM model, we find $S_8 \equiv \sigma_8 (\Omega_m/0.3)^{0.5}
=0.776^{+0.032}_{-0.033}$, which is in excellent agreement with the constraints
from the other HSC Year 3 cosmology analyses, as well as those from a number of
other cosmic shear experiments. This result implies a $\sim$$2\sigma$-level
tension with the Planck 2018 cosmology. We study the effect that various
systematic errors and modeling choices could have on this value, and find that
they can shift the best-fit value of $S_8$ by no more than $\sim$$0.5\sigma$,
indicating that our result is robust to such systematics.
