We describe a new method that can measure the true redshift distribution of any set of objects that are studied only photometrically. Measuring the angular cross-correlation between objects in the photometric sample with objects in some spectroscopic sample as a function of the spectroscopic image, along with other, standard correlation measurements, provides sufficient information to reconstruct the redshift distribution of the photometric sample. The spectroscopic sample need not resemble the photometric sample in galaxy properties, but must fall within its sky coverage. We test this hybrid, photometric-spectroscopic cross-correlation technique with Monte Carlo simulations based on realistic error estimates (including sample variance). The rms errors in recovering both the mean redshift and image of the redshift distribution for a single photometric redshift bin with true distribution given by a Gaussian are image, where image is the true Gaussian image is the surface density of the photometric sample in galaxies arcmin super(-2), and image is the number of galaxies with a spectroscopic redshift per unit image. We test the impact of non-Gaussian redshift outliers and of systematic errors due to unaccounted-for bias evolution, errors in measuring autocorrelations, photometric zero-point variations, or mistaken cosmological assumptions, and find that none will dominate measurement uncertainties in reasonable scenarios. The true redshift distributions of even arbitrarily faint photometric samples may be determined to the precision required by proposed dark energy experiments (image at image) with this method.