Narrow-band imaging surveys aimed at detecting the faint emission from the 5007 Å [ O III ] line of intracluster planetary nebulae in Virgo also probe high redshift z \sim 3.1 Ly \alpha emitters . Here we report on the spectroscopic identification of 9 Ly \alpha emitters at z = 3.13 with fluxes between 2 \times 10 ^ { -17 } and 2 \times 10 ^ { -16 } erg cm ^ { -2 } s ^ { -1 } obtained with the FORS spectrograph at Unit 1 of the ESO Very Large Telescope ( VLT UT1 ) . The spectra of these high redshift objects show a narrow , isolated Ly \alpha emission with very faint ( frequently undetected ) continuum , indicating a large equivalent width . No other features are visible in our spectra . Our Ly \alpha emitters are quite similar to those found by Hu ( 1998 ) , Cowie & Hu ( 1998 ) and Hu et al . ( 1998 ) . For a flat universe with H _ { 0 } =70 km s ^ { -1 } Mpc ^ { -1 } and q _ { 0 } =0.5 ( \Omega _ { \Lambda } =0 ) , the Ly \alpha luminosity of the brightest source is 1.7 \times 10 ^ { 9 } L \odot , and the comoving space density of the Ly \alpha emitters in the searched volume is 5 \times 10 ^ { -3 } Mpc ^ { -3 } . Using simple population synthesis models , on the assumption that these sources are regions of star formation , we conclude that the nebulae are nearly optically thick and must have a very low dust content , in order to explain the high observed Ly \alpha equivalent widths . For the cosmological and star formation parameters we adopted , the total stellar mass produced would seem to correspond to the formation of rather small galaxies , some of which are perhaps destined to merge . However , one of our sources might become a serious candidate for a proto-giant spheroidal galaxy if we assumed continuous star formation , a low mass cutoff of 0.1 M \odot in the IMF , and a flat accelerating universe with \Omega _ { 0 } =0.2 and \Omega _ { \Lambda } =0.8 . The implied star formation density in our sampled comoving volume is probably somewhat smaller than , but of the same order of magnitude as the star formation density at z \sim 3 derived by other authors from Lyman-break galaxy surveys . This result agrees with the expectation that the Ly \alpha emitters are a low-metallicity ( or low-dust ) tail in a distribution of star forming regions at high redshifts . Finally , the Ly \alpha emitters may contribute as many H-ionizing photons as QSOs at z \sim 3 . They are therefore potentially significant for the ionization budget of the early universe .