  We perform a blinded cosmology analysis with cosmic shear two-point
correlation functions (2PCFs) measured from more than 25 million galaxies in
the Hyper Suprime-Cam three-year shear catalog in four tomographic redshift
bins ranging from 0.3 to 1.5. After conservative masking and galaxy selection,
the survey covers 416 deg$^2$ of the northern sky with an effective galaxy
number density of 15 arcmin$^{-2}$ over the four redshift bins. The 2PCFs
adopted for cosmology analysis are measured in the angular range: $7.1 <
\theta/{\rm arcmin} < 56.6$ for $\xi_+$ and $31.2 <\theta/{\rm arcmin} < 248$
for $\xi_-$, with a total signal-to-noise ratio of 26.6. We apply a
conservative, wide, flat prior on the photometric redshift errors on the last
two tomographic bins, and the relative magnitudes of the cosmic shear amplitude
across four redshift bins allow us to calibrate the photometric redshift
errors. With this flat prior on redshift errors, we find $\Omega_{\rm
m}=0.256_{-0.044}^{+0.056}$ and $S_8\equiv \sigma_8 \sqrt{\Omega_{\rm
m}/0.3}=0.769_{-0.034}^{+0.031}$ (both 68\% CI) for a flat $\Lambda$ cold dark
matter cosmology. We find, after unblinding, that our constraint on $S_8$ is
consistent with the Fourier space cosmic shear and the 3$\times$2pt analyses on
the same HSC dataset. We carefully study the potential systematics from
astrophysical and systematic model uncertainties in our fiducial analysis using
synthetic data, and report no biases (including projection bias in the
posterior space) greater than $0.5\sigma$ in the estimation of $S_8$. Our
analysis hints that the mean redshifts of the two highest tomographic bins are
higher than initially estimated. In addition, a number of consistency tests are
conducted to assess the robustness of our analysis. Comparing our result with
Planck-2018 cosmic microwave background observations, we find a ~$2\sigma$
tension for the $\Lambda$CDM model.
