  We use a sample of 532 star-forming galaxies at redshifts $z\sim 1.4-2.6$
with deep rest-frame optical spectra from the MOSFIRE Deep Evolution Field
(MOSDEF) survey to place the first constraints on the nebular attenuation curve
at high redshift. Based on the first five low-order Balmer emission lines
detected in the composite spectra of these galaxies (${\rm H\alpha}$ through
${\rm H\epsilon}$), we derive a nebular attenuation curve that is similar in
shape to that of the Galactic extinction curve, suggesting that the dust
covering fraction and absorption/scattering properties along the lines-of-sight
to massive stars at high redshift are similar to those of the average Milky Way
sightline. The curve derived here implies nebular reddening values that are on
average systematically larger than those derived for the stellar continuum. In
the context of stellar population synthesis models that include the effects of
stellar multiplicity, the difference in reddening of the nebular lines and
stellar continuum may imply molecular cloud crossing timescales that are a
factor of $\gtrsim 3\times$ longer than those inferred for local molecular
clouds, star-formation rates that are constant or increasing with time such
that newly-formed and dustier OB associations always dominate the ionizing
flux, and/or that the dust responsible for reddening the nebular emission may
be associated with non-molecular (i.e., ionized and neutral) phases of the ISM.
Our analysis points to a variety of investigations of the nebular attenuation
curve that will be enabled with the next generation of ground- and space-based
facilities.
