  We present results on the dust attenuation curve of z~2 galaxies using early
observations from the MOSFIRE Deep Evolution Field (MOSDEF) survey. Our sample
consists of 224 star-forming galaxies with nebular spectroscopic redshifts in
the range z= 1.36-2.59 and high S/N measurements of, or upper limits on, the
H-alpha and H-beta emission lines obtained with Keck/MOSFIRE. We construct
composite SEDs of galaxies in bins of specific SFR and Balmer optical depth in
order to directly constrain the dust attenuation curve from the UV through
near-IR for typical star-forming galaxies at high redshift. Our results imply
an attenuation curve that is very similar to the SMC extinction curve at
wavelengths redward of 2500 Angstroms. At shorter wavelengths, the shape of the
curve is identical to that of the Calzetti relation, but with a lower
normalization (R_V). Hence, the new attenuation curve results in SFRs that are
~20% lower, and log stellar masses that are 0.16 dex lower, than those obtained
with the Calzetti attenuation curve. Moreover, we find that the difference in
the reddening---and the total attenuation---of the ionized gas and stellar
continuum correlates strongly with SFR, such that for dust-corrected SFRs
larger than 20 Msun/yr assuming a Chabrier IMF, the nebular emission lines
suffer an increasing degree of obscuration relative to the continuum. A simple
model that can account for these trends is one in which the UV through optical
stellar continuum is dominated by a population of less reddened stars, while
the nebular line and bolometric luminosities become increasingly dominated by
dustier stellar populations for galaxies with large SFRs, as a result of the
increased dust enrichment that accompanies such galaxies. Consequently, UV- and
SED-based SFRs may underestimate the total SFR at even modest levels of ~20
Msun/yr. [Abridged]
