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(abridged) We present kinematic results for a sample of 387 stars locatednear Leo I based on spectra obtained with the MMT's Hectochelle spectrographnear the MgI/Mgb lines. We estimate the mean velocity error of our sample to be2.4 km/s, with a systematic error of < 1 km/s. We produce a final sample of 328Leo I red giant members, from which we measure a mean heliocentric radialvelocity of 282.9 +/- 0.5 km/s, and a mean radial velocity dispersion of 9.2+/- 0.4 km/s for Leo I. The dispersion profile of Leo I is flat out to beyondits classical `tidal' radius. We fit the profile to a variety of equilibriumdynamical models and can strongly rule out models where mass follows light.Two-component Sersic+NFW models with tangentially anisotropic velocitydistributions fit the dispersion profile well, with isotropic models ruled outat a 95% confidence level. The mass and V-band mass-to-light ratio of Leo Iestimated from equilibrium models are in the ranges 5-7 x 10^7 M_sun and 9-14(solar units), respectively, out to 1 kpc from the galaxy center. Leo I memberslocated outside a `break radius' (about 400 arcsec = 500 pc) exhibitsignificant velocity anisotropy, whereas stars interior appear to haveisotropic kinematics. We propose the break radius represents the location ofthe tidal radius of Leo I at perigalacticon of a highly elliptical orbit. Ourscenario can account for the complex star formation history of Leo I, thepresence of population segregation within the galaxy, and Leo I's large outwardvelocity from the Milky Way. The lack of extended tidal arms in Leo I suggeststhe galaxy has experienced only one perigalactic passage with the Milky Way,implying that Leo I may have been injected into its present orbit by a thirdbody a few Gyr before perigalacticon.

The Velocity Dispersion Profile of the Remote Dwarf Spheroidal Galaxy Leo I: A Tidal Hit and Run?