K2-138 is a moderately bright (V = 12.2, K = 10.3) main-sequence K star observed in Campaign 12 of the NASA K2 mission. It hosts five small (1.6–3.3 ${R}_{\oplus }$) transiting planets in a compact architecture. The periods of the five planets are 2.35, 3.56, 5.40, 8.26, and 12.76 days, forming an unbroken chain of near 3:2 resonances. Although we do not detect the predicted 2–5 minute transit timing variations (TTVs) with the K2 timing precision, they may be observable by higher-cadence observations with, for example, Spitzer or CHEOPS. The planets are amenable to mass measurement by precision radial velocity measurements, and therefore K2-138 could represent a new benchmark system for comparing radial velocity and TTV masses. K2-138 is the first exoplanet discovery by citizen scientists participating in the Exoplanet Explorers project on the Zooniverse platform.