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We present Hubble Space Telescope images and 2 years of optical photometry of the quadruple quasar HE 0435-1223. The time delays between the intrinsic quasar variations are Δt_AD = -14.37 ^.75 _-.85, Δt_AB = -8.00^.73 _-.82, and Δt_AC = -2.10 ^.78 _-.71 days. We also observed nonintrinsic variations of ~0.1 mag yr^-1 that we attribute to microlensing. Instead of the traditional approach of assuming a rotation curve for the lens galaxy and then deriving the Hubble constant (H_0), we assume H_0 = (72 ± 7) km s^-1 Mpc^-1 and derive constraints on the rotation curve. On the scale over which the lensed images occur (1". = 5 h^-1 kpc ~- 1.5R_e), the lens galaxy must have a rising rotation curve, and it cannot have a constant mass-to-light ratio. These results add to the evidence that the structures of early-type galaxies are heterogeneous.