The recent discoveries of Jupiter-mass planets around nearby stars by measurement of stellar reaction motion (Mayor et al., 1995; Marcy and Butler, 1996) may be viewed as the beginning of a new era for ground-based astronomy. The next step is to obtain direct images of giant planets around nearby stars. In this paper, we show that this goal can be met by using adaptive optics (AO) on the new large telescopes with very smooth primary mirrors. Detailed simulations of an advanced AO system show that a Jupiter twin at 10 pc can be detected at 5 standard deviations above the residual halo noise in a single night of observation. With Gatewood's recent discovery (Gatewood, 1996) of a Jupiter mass planet at 2.5 AU orbiting Lalande 21185, there is now a perfect target for the first application of the new technique. This and other nearby stars will be imaged in a survey planned for the new single-mirror 6.5 m MMT and its twin Magellan telescope in Chile.