  Star-forming galaxies form a sequence in the [OIII]/H-beta vs. [NII]/H-alpha
diagnostic diagram, with low metallicity, highly ionized galaxies falling in
the upper left corner. Drawing from a large sample of UV-selected star-forming
galaxies at z~2 with rest-frame optical nebular emission line measurements from
Keck-MOSFIRE, we select the extreme ~5% of the galaxies lying in this upper
left corner, requiring log([NII]/H-alpha) <= 1.1 and log([OIII]/H-beta) >=
0.75. These cuts identify galaxies with 12 + log(O/H) <~ 8.0, when oxygen
abundances are measured via the O3N2 diagnostic. We study the Ly-alpha
properties of the resulting sample of 14 galaxies. The mean (median) rest-frame
Ly-alpha equivalent width is 39 (36) A, and 11 of the 14 objects (79%) are
Ly-alpha-emitters (LAEs) with W_Lya > 20 A. We compare the equivalent width
distribution of a sample of 522 UV-selected galaxies at 2.0<z<2.6 identified
without regard to their optical line ratios; this sample has mean (median)
Ly-alpha equivalent width -1 (-4) A, and only 9% of these galaxies qualify as
LAEs. The extreme galaxies typically have lower attenuation at Ly-alpha than
those in the comparison sample, and have ~50% lower median oxygen abundances.
Both factors are likely to facilitate the escape of Ly-alpha: in less dusty
galaxies Ly-alpha photons are less likely to be absorbed during multiple
scatterings, while the harder ionizing spectrum and higher ionization parameter
associated with strong, low metallicity star formation may reduce the covering
fraction or column density of neutral hydrogen, further easing Ly-alpha escape.
The use of nebular emission line ratios may prove useful in the identification
of galaxies with low opacity to Ly-alpha photons across a range of redshifts.
