Wolf-Rayet stars represent one of the final stages of massive stellar evolution. Relatively little is known about this short-lived phase and we currently lack reliable mass, distance, and binarity determinations for a representative sample. Here we report the first visual orbit for WR 140(=HD193793), a WC7+O5 binary system known for its periodic dust production episodes triggered by intense colliding winds near periastron passage. The IOTA and CHARA interferometers resolved the pair of stars in each year from 2003--2009, covering most of the highly-eccentric, 7.9 year orbit. Combining our results with the recent improved double-line spectroscopic orbit of Fahed et al. (2011), we find the WR 140 system is located at a distance of 1.67 +/- 0.03 kpc, composed of a WR star with M_WR = 14.9 +/- 0.5 Msun and an O star with M_O = 35.9 +/- 1.3 Msun. Our precision orbit yields key parameters with uncertainties times 6 smaller than previous work and paves the way for detailed modeling of the system. Our newly measured flux ratios at the near-infrared H and Ks bands allow an SED decomposition and analysis of the component evolutionary states.