We report the first results of AS2UDS : an 870 \mu m continuum survey with the Atacama Large Millimeter/Submillimeter Array ( ALMA ) of a total area of \sim 50 arcmin ^ { 2 } comprising a complete sample of 716 submillimeter sources drawn from the SCUBA-2 Cosmology Legacy Survey ( S2CLS ) map of the UKIDSS/UDS field . The S2CLS parent sample covers a 0.96 degree ^ { 2 } field at \sigma _ { 850 } = 0.90 \pm 0.05 mJy beam ^ { -1 } . Our deep , high-resolution ALMA observations with \sigma _ { 870 } \sim 0.25 mJy and a 0 \farcs 15–0 \farcs 30 FWHM synthesized beam , provide precise locations for 695 submillimeter galaxies ( SMGs ) responsible for the submillimeter emission corresponding to 606 sources in the low resolution , single-dish map . We measure the number counts of SMGs brighter than S _ { 870 } \geq 4 mJy , free from the effects of blending and show that the normalisation of the counts falls by 28 \pm 2 % in comparison to the SCUBA-2 parent sample , but that the shape remains unchanged . We determine that 44 ^ { +16 } _ { -14 } % of the brighter single-dish sources with S _ { 850 } \geq 9 mJy consist of a blend of two or more ALMA-detectable SMGs brighter than S _ { 870 } \sim 1 mJy ( corresponding to a galaxy with a total-infrared luminosity of L _ { IR } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 % pt \hbox { { $ \scriptstyle \sim$ } } } 10 ^ { 12 } L _ { \odot } ) , in comparison to 28 \pm 2 % for the single-dish sources at S _ { 850 } \geq 5 mJy . Using the 46 single-dish submillimeter sources that contain two or more ALMA-detected SMGs with photometric redshifts , we show that there is a significant statistical excess of pairs of SMGs with similar redshifts ( < 1 % probability of occurring by chance ) , suggesting that at least 30 % of these blends arise from physically associated pairs of SMGs .