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 (1.6-3.3R_Earth) transiting planets in a compact architecture. The periods of the five planets are 2.35 d, 3.56 d, 5.40 d, 8.26 d, and 12.76 d, forming an unbroken chain of near 3:2 resonances. Although we do not detect the predicted 2-5 minute transit timing variations 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 systems 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.