We present interferometric observations of N2H+ (1-0) in the starless, dense core L1544 in Taurus. Redshifted self-absorption, indicative of inward motions, is found toward the center of an elongated core. The data are fit by a nonspherical model consisting of two isothermal, rotating, centrally condensed layers. Through a hybrid global-individual fit to the spectra, we map the variation of infall speed at scales ~1400 AU and find values ~0.08 km s-1 around the core center. The inward motions are small in comparison to thermal, rotational, and gravitational speeds but are large enough to suggest that L1544 is very close to forming a star.