Spectroscopic observations from the Large Binocular Telescope and the Very Large Telescope reveal kinematically narrow lines ( \sim 50 ~ { } \ > { km } { s } ^ { -1 } ) for a sample of 14 Extreme Emission Line Galaxies ( EELGs ) at redshifts 1.4 < z < 2.3 . These measurements imply that the total dynamical masses of these systems are low ( \lesssim 3 \times 10 ^ { 9 } ~ { } M _ { \odot } ) . Their large [ O III ] \lambda 5007 equivalent widths ( 500 - 1100 Å ) and faint blue continuum emission imply young ages of 10 - 100 Myr and stellar masses of 10 ^ { 8 } -10 ^ { 9 } ~ { } M _ { \odot } , confirming the presence of a violent starburst . The dynamical masses represent the first such determinations for low-mass galaxies at z > 1 . The stellar mass formed in this vigorous starburst phase represents a large fraction of the total ( dynamical ) mass , without a significantly massive underlying population of older stars . The occurrence of such intense events in shallow potentials strongly suggests that supernova-driven winds must be of critical importance in the subsequent evolution of these systems .