We present the results of a radial velocity survey of planetary nebulae (PNs) in the normal elliptical galaxy NGC 3379 performed with the Kitt Peak 4m telescope and the NESSIE multifiber spectrograph. In two half-nights, we measured 29 PNs with projected galactocentric distances between 0.4 and 3.8 effective radii (1<R<10kpc) with an observational uncertainty of ~7km/s. These data extend 3 times further into the halo than any previous absorption-line velocity study. The velocity dispersion and photometric profile of the galaxy agrees extremely well with that expected from a constant mass-to-light ratio, isotropic orbit Jaffe model with M/L_B_~7; the best-fitting anisotropic models from a quadratic programming algorithm also give M/L_B_~7. The data are consistent with models that contain no dark matter within 3.5 effective radii of the galaxy's nucleus.