The intermediate-frequency peaked BL Lacertae (IBL) object 3C 66A is detected during 2007-2008 in VHE ( very high energy; E > 100 GeV) gamma rays with the VERITAS stereoscopic array of imaging atmospheric Cherenkov telescopes. An excess of 1791 events is detected, corresponding to a significance of 21.2 standard deviations (sigma), in these observations (32.8 hr live time). The observed integral flux above 200 GeV is 6% of the Crab Nebula's flux and shows evidence for variability on the timescale of days. The measured energy spectrum is characterized by a soft power law with photon index Gamma = 4.1 +/- 0.4(stat) +/- 0.6(sys). The radio galaxy 3C 66B is excluded as a possible source of the VHE emission.