  Using VLT/X-shooter we searched for emission line galaxies associated to four
damped Lyman-$\alpha$ systems (DLAs) and one sub-DLA at 2.73<=z<=3.25 towards
QSO J2358+0149. We detect [O III] emission from a "low-cool" DLA at z_abs =
2.9791 (having log N(HI)=21.69+\-0.10, [Zn/H] = -1.83+\-0.18) at an impact
parameter of, $\rho$ ~12 kpc. The associated galaxy is compact with a dynamical
mass of (1-6)x10^9 M_solar, very high excitation ([O III]/[O II] and [O
III]/[H$\beta$] both greater than 10), 12+[O/H]<=8.5 and moderate star
formation rate (SFR <=2 M_solar yr^{-1}). Such properties are typically seen in
the low-z extreme blue compact dwarf galaxies. The kinematics of the gas is
inconsistent with that of an extended disk and the gas is part of either a
large scale wind or cold accretion. We detect Ly$\alpha$ emission from the
z_abs = 3.2477 DLA (having log N(HI)=21.12+\-0.10 and [Zn/H]=-0.97+\-0.13).The
Ly$\alpha$ emission is redshifted with respect to the metal absorption lines by
320 km s^{-1}, consistent with the location of the red hump expected in
radiative transport models. We derive SFR ~0.2-1.7 M_solar yr^{-1} and
Ly$\alpha$ escape fraction of >=10 per cent. No other emission line is detected
from this system. Because the DLA has a small velocity separation from the
quasar (~500 km s^{-1}) and the DLA emission is located within a small
projected distance ($\rho<5$ kpc), we also explore the possibility that the
Ly$\alpha$ emission is being induced by the QSO itself. QSO induced Ly$\alpha$
fluorescence is possible if the DLA is within a physical separation of 340 kpc
to the QSO. Detection of stellar continuum light and/or the oxygen emission
lines would disfavor this possibility. We do not detect any emission line from
the remaining three systems.
