Intensive monitoring of the innermost jet in the quasar 3C 279 at 43 GHz from 1998 March to 2001 April with the Very Long Baseline Array, in combination with previous observations, reveal (1) an increase in apparent speed from 5c to 17c and (2) a change in projected direction of the jet by ∼ 20°. These effects could result from a small increase in the intrinsic viewing angle of the jet nozzle from Θ ≲ 0°.5 to Θ ≲ 1°.6, with no increase required in the actual speed of the flow, which corresponds to a Lorentz factor γ ≳ 20. The Lorentz factor ∼20 and viewing angle ∼0°.5 imply that the Doppler factor is at least 39 close to the core; this extreme value explains the high flux density and rapid variability of 3C 279 across the electromagnetic spectrum.