  Photometric redshifts are a key component of many science objectives in the
Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). In this paper, we
describe and compare the codes used to compute photometric redshifts for
HSC-SSP, how we calibrate them, and the typical accuracy we achieve with the
HSC five-band photometry (grizy). We introduce a new point estimator based on
an improved loss function and demonstrate that it works better than other
commonly used estimators. We find that our photo-z's are most accurate at
0.2<~zphot<~1.5, where we can straddle the 4000A break. We achieve
sigma(d_zphot/(1+zphot))~0.05 and an outlier rate of about 15% for galaxies
down to i=25 within this redshift range. If we limit to a brighter sample of
i<24, we achieve sigma~0.04 and ~8% outliers. Our photo-z's should thus enable
many science cases for HSC-SSP. We also characterize the accuracy of our
redshift probability distribution function (PDF) and discover that some codes
over/under-estimate the redshift uncertainties, which have implications for
N(z) reconstruction. Our photo-z products for the entire area in the Public
Data Release 1 are publicly available, and both our catalog products (such as
point estimates) and full PDFs can be retrieved from the data release site,
https://hsc-release.mtk.nao.ac.jp/.
