We report the detection of very-high-energy (VHE) gamma-ray emission from supernova remnant (SNR) G106.3+2.7. Observations performed in 2008 with the VERITAS atmospheric Cherenkov gamma-ray telescope resolve extended emission overlapping the elongated radio SNR. The 7.3 sigma (pre-trials) detection has a full angular extent of roughly 0.6deg by 0.4deg. Most notably, the centroid of the VHE emission is centered near the peak of the coincident 12CO (J = 1-0) emission, 0.4deg away from the pulsar PSR J2229+6114, situated at the northern end of the SNR. Evidently the current-epoch particles from the pulsar wind nebula are not participating in the gamma-ray production. The VHE energy spectrum measured with VERITAS is well characterized by a power law dN/dE = N_0(E/3 TeV)^{-G} with a differential index of G = 2.29 +/- 0.33stat +/- 0.30sys and a flux of N_0 = (1.15 +/- 0.27stat +/- 0.35sys)x 10^{-13} cm^{-2} s^{-1} TeV^{-1}. The integral flux above 1 TeV corresponds to ~5 percent of the steady Crab Nebula emission above the same energy. We describe the observations and analysis of the object and briefly discuss the implications of the detection in a multiwavelength context.