We observed the pre-stellar core L1521F in dust emission at 1.2mm and in two transitions each of N2H+, N2D+, C18O, and C17O in order to increase the sample of well studied centrally concentrated and chemically evolved starless cores, likely on the verge of star formation, and to determine the initial conditions for low--mass star formation in the Taurus Molecular Cloud. We derived in this object a molecular hydrogen number density n(H2) ~ 10^6 cm-3 and a CO depletion factor, integrated along the line of sight, fD ~ 15 in the central 20, similar to the pre-stellar core L1544. However, the N(N2D+)/N(N2H+) column density ratio is ~0.1, a factor of about 2 lower than that found in L1544. The observed relation between the deuterium fractionation and the integrated CO depletion factor across the core can be reproduced by chemical models if N2H+ is slightly (factor of ~2 in fractional abundance) depleted in the central 3000 AU. The N2H+ and N2D+ linewidths in the core center are ~0.3 km/s, significantly larger than in other more quiescent Taurus starless cores but similar to those observed in the center of L1544. The kinematical behaviour of L1521F is more complex than seen in L1544, and a model of contraction due to ambipolar diffusion is only marginally consistent with the present data. Other velocity fields, perhaps produced by unresolved substructure, are present. Both chemical and kinematical analyses suggest that L1521F is less evolved than L1544, but, in analogy with L1544, it is approaching the ``critical state.
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