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-zs 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-zs 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/.
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