Recent results from the Planetary Nebula Spectrograph (PN.S) survey have revealed a rapidly falling velocity dispersion profile in the nearby elliptical galaxy NGC 3379, casting doubts on whether this intermediate-luminosity galaxy has the kind of dark matter halo expected in LambdaCDM cosmology. We present a detailed dynamical study of this galaxy, combining long-slit spectroscopy, SAURON integral-field data, and PN.S velocities, reaching to more than seven effective radii (R_e). We construct spherical and axisymmetric dynamical models for these data with the flexible made-to-measure NMAGIC code, in a sequence of gravitational potentials with varying dark halo mass. We find that the data are consistent both with near-isotropic spherical systems dominated by the stellar mass, and with models in massive halos with strongly radially anisotropic outer parts (beta >~ 0.8 at 7R_e). Formal likelihood limits would exclude (at 1 sigma) the model with stars only, as well as halo models with v_circ(7R_e) >~ 250 km/s. A sequence of more realistic axisymmetric models of different inclinations and a small number of triaxial tests confirm the spherical results. All valid models fitting all the data are dynamically stable over Gyrs, including the most anisotropic ones. NGC 3379 may well have a dark matter halo as predicted by recent merger models within LambdaCDM cosmology, provided its outer envelope is strongly radially anisotropic. (abridged)
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