We present near-infrared spectroscopy of a sample of 22 Extreme Emission Line Galaxies at redshifts 1.3 < z < 2.3, confirming that these are low-mass (M* = 10^8 - 10^9 M_sun) galaxies undergoing intense starburst episodes (M*/SFR ~ 10-100 Myr). The sample is selected by [O III] or H{\alpha} emission line flux and equivalent width using near-infrared grism spectroscopy from the 3D-HST survey. High-resolution NIR spectroscopy is obtained with LBT/LUCI and VLT/X-SHOOTER. The [O III]/H{\beta} line ratio is high (> 5) and [N II]/H{\alpha} is always significantly below unity, which suggests a low gas-phase metallicity. We are able to determine gas-phase metallicities for 7 of our objects using various strong-line methods, with values in the range 0.05-0.30 Z_sun and with a median of 0.15 Z_sun; for 3 of these objects we detect [O III]{\lambda}4363 which allows for a direct constraint on the metallicity. The velocity dispersion, as measured from the nebular emission lines, is typically ~50 km/s. Combined with the observed star-forming activity, the Jeans and Toomre stability criteria imply that the gas fraction must be large (> 2/3), consistent with the difference between our dynamical and stellar mass estimates. The implied gas depletion time scale (several hundred Myr) is substantially longer than the inferred mass-weighted ages (~50 Myr), which further supports the emerging picture that most stars in low-mass galaxies form in short, intense bursts of star formation.
Comment: Resubmitted to ApJ after first referee report, 18 pages, 14 figures, 4 tables