Using high-resolution microwave sky maps made by the Atacama Cosmology Telescope, we for the first time present strong evidence for motions of galaxy clusters and groups via microwave background temperature distortions due to the kinematic Sunyaev-Zel'dovich effect. Galaxy clusters are identified by their constituent luminous galaxies observed by the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. We measure the mean pairwise momentum of clusters, with a probability of the signal being due to random errors of 0.002, and the signal is consistent with the growth of cosmic structure in the standard model of cosmology. DOI: 10.1103/PhysRevLett.109.041101 PACS numbers: 98.80.Es, 98.62.Py, 98.65.Cw, 98.70.Vc PRL 109, 041101 (2012 Selected for a Viewpoint in Physics P H Y S I C A L R E V I E W L E T T E R S week ending 0031-9007=12=109(4)=041101 (6) 041101-1 Ó 2012 American Physical SocietyIntroduction.-The growth of cosmic structure over the history of the Universe inevitably results not only in the formation of dense objects, but also in motions of these objects. Measurements of these motions have the potential to provide both a valuable consistency check on the standard cosmological model, and also an independent route to constraining cosmological parameters and the nature of dark energy.In 1972, Sunyaev and Zel'dovich realized that a moving galaxy cluster, which is largely composed of hot, ionized gas in a dark matter potential well, will induce a small brightness temperature shift in the microwave radiation passing through it. The shift is proportional to both the mass in electrons and the line-of-sight velocity of the cluster with respect to the microwave background rest frame [1,2]. This kinematic Sunyaev-Zel'dovich (kSZ) effect is distinct from the thermal SZ (tSZ) effect, in which scattering from the same hot cluster gas creates a spectral distortion (see [3] for a review). In high-mass clusters (M ' 10 15 solar masses), the tSZ signal is typically a factor of 20 larger than the kSZ signal; however, the two signals are comparable for the lowmass clusters (M ' 10 13 M ) which are far more abundant. (For brevity, we refer to any object with mass larger than 10 13 M as a cluster, even though objects below 10 14 M are usually referred to as ''groups.'') The tSZ effect from large clusters is now regularly observed in blind surveys [4][5][6][7], but only upper limits for the kSZ effect from individual galaxy clusters have been achieved to date [8][9][10][11][12].In this Letter, we present clear statistical evidence of the motions of galaxy clusters through their kSZ signal in arcminute-resolution microwave maps made with the Atacama Cosmology Telescope (ACT) [13]. Luminous galaxies are associated with galaxy clusters [14,15], and we use the Sloan Digital Sky Survey III (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) [16] catalog of these galaxies as galaxy cluster proxies, giving the sky location and redshift for thousands of potential clusters. We then treat the effe...