We present a wide-field (4.5 deg^2) photometric and spectroscopic survey of the Leo I dwarf spheroidal (dSph) galaxy to explore its extended morphology and dynamics. As in previous papers in this series, we take advantage of photometry in the M, T_2, and DDO51 filter system to select LeoI red giant branch star candidates, and, so far, this selection technique has proven 100% reliable in selecting actual Leo I members among more than 100 M < 21.5 Leo I giant candidates having previous or new Keck DEIMOS spectroscopy to a radius >1.3 times the limiting radius of the fitted, central King profile. The two-dimensional distribution of all similarly-selected Leo I giant candidates is well fitted by a central single-component King profile of limiting radius 13.3 arcmin, but many giant stars are found outside this newly derived King limiting radius. The density profile thus shows a break at a major axis radial distance of ~10 arcmin produced by an excess of stars at and beyond the King limiting radius (spectroscopically confirmed to be made of true Leo I members), and primarily along the major axis of the main body of the rather elongated satellite. This spatial configuration, a rather flat velocity dispersion profile and an asymmetric radial velocity (RV) distribution among the Leo I members at large radii together support a picture where Leo I has been tidally disrupted on at least one, but at most two, perigalactic passages of a massive Local Group member. (abridged)
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