  We present optical (UBVRI) and near-infrared (YJHK) photometry of the normal
Type Ia supernova 2004S. We also present eight optical spectra and one near-IR
spectrum of SN 2004S. The light curves and spectra are nearly identical to
those of SN 2001el. This is the first time we have seen optical and IR light
curves of two Type Ia supernovae match so closely. Within the one parameter
family of light curves for normal Type Ia supernovae, that two objects should
have such similar light curves implies that they had identical intrinsic colors
and produced similar amounts of Ni-56. From the similarities of the light curve
shapes we obtain a set of extinctions as a function of wavelength which allows
a simultaneous solution for the distance modulus difference of the two objects,
the difference of the host galaxy extinctions, and R_V. Since SN 2001el had
roughly an order of magnitude more host galaxy extinction than SN 2004S, the
value of R_V = 2.15 (+0.24 -0.22) pertains primarily to dust in the host galaxy
of SN 2001el. We have also shown via Monte Carlo simulations that adding rest
frame J-band photometry to the complement of BVRI photometry of Type Ia SNe
decreases the uncertainty in the distance modulus by a factor of 2.7. A
combination of rest frame optical and near-IR photometry clearly gives more
accurate distances than using rest frame optical photometry alone.
