As part of an effort to observe high-energy γ-ray blazars with VLBI, we have produced 8 and 2 GHz VLBI images, at eight epochs, of the quasar 1611+343, which has been detected by the EGRET telescope on board the Compton Gamma Ray Observatory. The VLBI data have been taken from the geodetic database of the Washington VLBI correlator. As is expected for a γ-ray quasar, we find that 1611+343 possesses a jet with several compact components moving at apparent superluminal speeds. We have detected five components and have measured speeds for the outer four of 6.7 +/- 1.6, 3.8 +/- 1.4, 7.6 +/- 1.3, and 11.5 +/- 2.3 h-1c from the outermost component inward. (H0 = 100 h km s-1 Mpc-1, q0 = 0.5.) By comparing the apparent superluminal expansion speeds with a lower limit to the Doppler beaming factor derived from X-ray observations, we have calculated an upper limit on the angle of the jet to the line of sight of θ <= 6.8d and a lower limit to the Lorentz factor of the components of Γ >= 7.1. We have mapped the two-dimensional projected structure of the VLBI jet and clearly see different trajectories for different components at the same distance from the core, which rules out a continuous jet model for this source. A possible connection is found between enhanced levels of γ-ray activity and the ejection of new VLBI components from the core.