We present the first millimeter-wave aperture synthesis map of dust around a main sequence star . A 3 ^ { \prime \prime } resolution image of 1.3 mm continuum emission from Vega reveals a clump of emission 12 ^ { \prime \prime } from the star at PA 45 ^ { \circ } , consistent with the location of maximum 850 \mu m emission in a lower resolution JCMT/SCUBA map . The flux density is 4.0 \pm 0.9 mJy . Adjacent 1.3 mm peaks with flux densities 3.4 \pm 1.0 mJy and 2.8 \pm 0.9 mJy are located 14 ^ { \prime \prime } and 13 ^ { \prime \prime } from the star at PA 67 ^ { \circ } and 18 ^ { \circ } , respectively . An arc-like bridge connects the two strongest peaks . There is an additional 2.4 \pm 0.8 mJy peak to the SW 11 ^ { \prime \prime } from the star at PA 215 ^ { \circ } and a marginal detection , 1.4 \pm 0.5 mJy , at the stellar position , consistent with photospheric emission . An extrapolation from the 850 \mu m flux , assuming F _ { 1.3 mm - 0.85 mm } \propto \lambda ^ { -2.8 } , agrees well with the total detected flux for Vega at 1.3 mm , and implies a dust emissivity index , \beta , of 0.8 We conclude that we have detected all but a very small fraction of the dust imaged by SCUBA in our aperture synthesis map and that these grains are largely confined to segments of a ring of radius 95 AU .