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Strong gravitational lenses with measured time delays between the multipleimages allow a direct measurement of the time-delay distance to the lens, andthus a measure of cosmological parameters, particularly the Hubble constant,$H_{0}$. We present a blind lens model analysis of the quadruply-imaged quasarlens HE 0435-1223 using deep Hubble Space Telescope imaging, updated time-delaymeasurements from the COSmological MOnitoring of GRAvItational Lenses(COSMOGRAIL), a measurement of the velocity dispersion of the lens galaxy basedon Keck data, and a characterization of the mass distribution along the line ofsight. HE 0435-1223 is the third lens analyzed as a part of the $H_{0}$ Lensesin COSMOGRAIL's Wellspring (H0LiCOW) project. We account for various sources ofsystematic uncertainty, including the detailed treatment of nearby perturbers,the parameterization of the galaxy light and mass profile, and the regions usedfor lens modeling. We constrain the effective time-delay distance to be$D_{\Delta t} = 2612_{-191}^{+208}~\mathrm{Mpc}$, a precision of 7.6%. From HE0435-1223 alone, we infer a Hubble constant of $H_{0} =73.1_{-6.0}^{+5.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$ assuming a flat $\Lambda$CDMcosmology. The cosmographic inference based on the three lenses analyzed byH0LiCOW to date is presented in a companion paper (H0LiCOW Paper V).

H0LiCOW IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology