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 degrees.6 by 0 degrees.4. Most notably, the centroid of the VHE emission is centered near the peak of the coincident (CO)-C-12 (J = 1-0) emission, 0 degrees.4 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)(-Gamma) with a differential index of Gamma = 2.29 +/- 0.33(stat) +/- 0.30(sys) and a flux of N-0 = (1.15 +/- 0.27(stat) +/- 0.35(sys)) x 10(-13) cm(-2) s(-1) TeV-1. The integral flux above 1 TeV corresponds to similar 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.