We present the first strong detection of very high energy γ-rays from the close (z = 0.048) X-ray-selected BL Lacertae object 1ES 1959+650. Observations were made with the Whipple 10 m telescope on Mount Hopkins, Arizona, using the atmospheric Cerenkov imaging technique. The flux between 2002 May and July was highly variable, with a mean of 0.64 ± 0.03 times the steady flux from the Crab Nebula and reaching a maximum of 5 crab, with variability on timescales as short as 7 hr.