Recent simulations have indicated that vinyl cyanide is the best candidate molecule for the formation of cell membranes/vesicle structures in Titan's hydrocarbon-rich lakes and seas. Although the existence of vinyl cyanide (C2H3CN) on Titan was previously inferred using Cassini mass spectrometry, a definitive detection has been lacking until now. We report the first spectroscopic detection of vinyl cyanide in Titan's atmosphere, obtained using archival data from the Atacama Large Millimeter/submillimeter Array (ALMA), collected from February to May 2014. We detect the three strongest rotational lines of C2H3CN in the frequency range of 230 to 232 GHz, each with >4σ confidence. Radiative transfer modeling suggests that most of the C2H3CN emission originates at altitudes of ≥200 km, in agreement with recent photochemical models. The vertical column densities implied by our best-fitting models lie in the range of 3.7 × 10^13 to 1.4 × 10^14 cm-2. The corresponding production rate of vinyl cyanide and its saturation mole fraction imply the availability of sufficient dissolved material to form ~10^7 cell membranes/cm3 in Titan's sea Ligeia Mare.