We present a detection of the unnormalized skewness 3(n̂)> induced by the thermal Sunyaev-Zel’dovich (tSZ) effect in filtered Atacama Cosmology Telescope (ACT) 148 GHz cosmic microwave background temperature maps. Contamination due to infrared and radio sources is minimized by template subtraction of resolved sources and by constructing a mask using outlying values in the 218 GHz (tSZ-null) ACT maps. We measure 3(n̂)>=-31±6  μK3 (Gaussian statistics assumed) or ±14  μK3 (including non-Gaussian corrections) in the filtered ACT data, a 5σ detection. We show that the skewness is a sensitive probe of σ8, and use analytic calculations and tSZ simulations to obtain cosmological constraints from this measurement. From this signal alone we infer a value of σ8=0.79-0.03+0.03 (68% C.L.) -0.06+0.06 (95% C.L.). Our results demonstrate that measurements of non-Gaussianity can be a useful method for characterizing the tSZ effect and extracting the underlying cosmological information.