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We have used interferometric and spectroscopic observations of HR 8257 to determine a three-dimensional orbit of the system. The orbit has a period of 12.21345 days and an eccentricity of 0.2895. The masses of the F0 and F2 dwarf components are 1.56 and 1.38 M☉, respectively, with fractional errors of 1.4%. Our orbital parallax of 13.632 ± 0.095 mas, corresponding to a distance of 73.4 ± 0.6 pc, differs from the Hipparcos result by just 2% and has a significantly smaller uncertainty. From our spectroscopic observations and spectral energy distribution modeling we determine the component effective temperatures and luminosities to be Teff(A) = 7030 ± 200 K and Teff(B) = 6560 ± 200 K and LA = 9.4 ± 0.3 L☉ and LB = 4.7 ± 0.2 L☉. The primary rotates pseudosynchronously, while the secondary is not far from its pseudosynchronous rotational velocity. Although both early-F stars are slowly rotating, neither component of this close binary is an Am star. A comparison with evolutionary tracks indicates that the stars are slightly metal poor, and although the components have evolved away from the zero-age main sequence, they are both still dwarfs.