We present CCD photometry and spectrographic observations for stars in the open cluster NGC 346, which excites the largest H II region in the Small Magellanic Cloud. These observations show that NGC 346 is an extremely young cluster, containing more than 20 hot O-type stars. A radial-velocity study of the brightest stars, and also of the nearby supergiant Of star Sk 80, discloses atmospheric expansion due to strong stellar winds, but no large-amplitude radial-velocity variations due to short-period binary motion. However, two stars are probably longer period binaries.