Large-field surveys of NH3, C2S, 13CO, and C18O in the L1551 dark cloud have revealed a prolate, pre-protostellar molecular core (L1551 MC) in a relatively quiescent region to the northwest of the well-known IRS 5 source. The kinetic temperature is measured to be 9 K, the total mass is ∼2 M☉, and the average particle density is 104-105/cm3. L1551 MC is 2'.25x1'.11 in projection, oriented at a position angle of 133°. The turbulent motions are on the order of the sound speed in the medium and contain 4% of the gravitational energy, Egrav, of the core. The angular momentum vector is projected along the major axis of L1551 MC, corresponding to a rotational energy of 2.5x10–3sin\ul -2i|Egrav|. The thermal energy constitutes about a third of|Egrav|, and the virial mass is approximately equal to the total mass. L1551 MC is gravitationally bound and in the absence of strong, ∼160 µG magnetic fields will likely contract on a ∼0.3 Myr timescale. The line profiles of many molecular species suggest that the cold quiescent interior is surrounded by a dynamic, perhaps infalling envelope that is embedded within the ambient molecular gas of L1551.