  We present results from Planetary Nebula Spectrograph (PN.S) observations of
the elliptical galaxy NGC 3379 and a description of the data reduction
pipeline. We detected 214 planetary nebulae of which 191 are ascribed to NGC
3379, and 23 to the companion galaxy NGC 3384. Comparison with data from the
literature show that the PN.S velocities have an internal error of <20km/s and
a possible offset of similar magnitude. We present the results of kinematic
modelling and show that the PN kinematics are consistent with absorption-line
data in the region where they overlap. The resulting combined kinematic data
set, running from the center of NGC 3379 out to more than seven effective radii
(Reff), reveals a mean rotation velocity that is small compared to the random
velocities, and a dispersion profile that declines rapidly with radius. From a
series of Jeans dynamical models we find the B-band mass-to-light ratio inside
5 Reff to be 8 to 12 in solar units, and the dark matter fraction inside this
radius to be less than 40%. We compare these and other results of dynamical
analysis with those of dark-matter-dominated merger simulations, finding that
significant discrepancies remain, reiterating the question of whether NGC 3379
has the kind of dark matter halo that the current LambdaCDM paradigm requires.
