We use a sample of 532 star-forming galaxies at redshifts $zsim 1.4-2.6$ 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 (${rm Halpha}$ through ${rm Hepsilon}$), 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 $gtrsim 3times$ 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.
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