We present new H-band echelle spectra, obtained with the NIRSPEC spectrograph at Keck II, for the massive star cluster B in the nearby dwarf irregular galaxy NGC 1569. From spectral synthesis and equivalent width measurements we obtain abundances and abundance patterns. We derive an Fe abundance of [Fe/H]=-0.63+/-0.08, a super-solar [alpha/Fe] abundance ratio of +0.31+/-0.09, and an O abundance of [O/H]=-0.29+/-0.07. We also measure a low 12C/13C = 5+/-1 isotopic ratio. Using archival imaging from the Advanced Camera for Surveys on board HST, we construct a colour-magnitude diagram (CMD) for the cluster in which we identify about 60 red supergiant (RSG) stars, consistent with the strong RSG features seen in the H-band spectrum. The mean effective temperature of these RSGs, derived from their observed colours and weighted by their estimated H-band luminosities, is 3790 K, in excellent agreement with our spectroscopic estimate of Teff = 3800+/-200 K. From the CMD we derive an age of 15-25 Myr, slightly older than previous estimates based on integrated broad-band colours. We derive a radial velocity of -78+/-3 km/s and a velocity dispersion of 9.6+/-0.3 km/s. In combination with an estimate of the half-light radius of 0.20+/-0.05 from the HST data, this leads to a dynamical mass of (4.4+/-1.1)E5 Msun. The dynamical mass agrees very well with the mass predicted by simple stellar population models for a cluster of this age and luminosity, assuming a normal stellar IMF. The cluster core radius appears smaller at longer wavelengths, as has previously been found in other extragalactic young star clusters.
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