We present the first resolved images of the eclipsing binary β Lyrae, obtained with the CHARA Array interferometer and the MIRC combiner in the H band. The images clearly show the mass donor and the thick disk surrounding the mass gainer at all six epochs of observation. The donor is brighter and generally appears elongated in the images, the first direct detection of photospheric tidal distortion due to Roche lobe filling. We also confirm expectations that the disk component is more elongated than the donor and is relatively fainter at this wavelength. Image analysis and model fitting for each epoch were used for calculating the first astrometric orbital solution for β Lyrae, yielding precise values for the orbital inclination and position angle. The derived semimajor axis also allows us to estimate the distance of β Lyrae; however, systematic differences between the models and the images limit the accuracy of our distance estimate to about 15%. To address these issues, we will need a more physical, self-consistent model to account for all epochs as well as the multiwavelength information from the eclipsing light curves.