  We identify an abundant population of extreme emission line galaxies (EELGs)
at redshift z~1.7 in the Cosmic Assembly Near-IR Deep Extragalactic Legacy
Survey (CANDELS) imaging from Hubble Space Telescope/Wide Field Camera 3
(HST/WFC3). 69 EELG candidates are selected by the large contribution of
exceptionally bright emission lines to their near-infrared broad-band
magnitudes. Supported by spectroscopic confirmation of strong [OIII] emission
lines -- with rest-frame equivalent widths ~1000\AA -- in the four candidates
that have HST/WFC3 grism observations, we conclude that these objects are
galaxies with 10^8 Msol in stellar mass, undergoing an enormous starburst phase
with M_*/(dM_*/dt) of only ~15 Myr. These bursts may cause outflows that are
strong enough to produce cored dark matter profiles in low-mass galaxies. The
individual star formation rates and the co-moving number density (3.7x10^-4
Mpc^-3) can produce in ~4 Gyr much of the stellar mass density that is
presently contained in 10^8-10^9 Msol dwarf galaxies. Therefore, our
observations provide a strong indication that many or even most of the stars in
present-day dwarf galaxies formed in strong, short-lived bursts, mostly at z>1.
