We report the detection of very high energy gamma-ray emission from the blazar S3 1227+25 (VER J1230+253) with the Very Energetic Radiation Imaging Telescope Array System (VERITAS). VERITAS observations of the source were triggered by the detection of a hard-spectrum GeV flare on 2015 May 15 with the Fermi-Large Area Telescope (LAT). A combined 5 hr VERITAS exposure on May 16 and 18 resulted in a strong 13σ detection with a differential photon spectral index, Γ = 3.8 ± 0.4, and a flux level at 9% of the Crab Nebula above 120 GeV. This also triggered target-of-opportunity observations with Swift, optical photometry, polarimetry, and radio measurements, also presented in this work, in addition to the VERITAS and Fermi-LAT data. A temporal analysis of the gamma-ray flux during this period finds evidence of a shortest variability timescale of τ_obs = 6.2 ± 0.9 hr, indicating emission from compact regions within the jet, and the combined gamma-ray spectrum shows no strong evidence of a spectral cutoff. An investigation into correlations between the multiwavelength observations found evidence of optical and gamma-ray correlations, suggesting a single-zone model of emission. Finally, the multiwavelength spectral energy distribution is well described by a simple one-zone leptonic synchrotron self-Compton radiation model.