WepresentspectroscopicobservationsobtainedwiththeESOVeryLargeTelecope ( VLT ) ofsevencandidateLy \alpha emittinggalaxiesinthefieldoftheradioquietQ1205-30atz=3.04previouslydetectedwithdeepnarrowbandimaging.BasedonequivalentwidthsandlimitsonlineratiosweconfirmthatallsevenobjectsareLy \alpha emittinggalaxies.DeepimagesalsoobtainedwiththeVLTintheBandIbandsshowthatfiveofthesevengalaxieshaveveryfaintcontinuumfluxes ( I ( AB ) \approx 26.8andB ( AB ) \approx 27.3 ) .Thestarformationratesofthesesevengalaxiesestimatedfromtherest-frameUVcontinuumaround2000Å , asprobedbytheI-banddetections , aswellasfromtheLy \alpha luminosities , are1–4M _ { \sun } yr ^ { -1 } assumingaHubbleconstantof65kms ^ { -1 } Mpc ^ { -1 } , \Omega _ { m } = 0.3 , and \Omega _ { \Lambda } = 0.7 .Thisis1–3ordersofmagnitudelowerthanforotherknownpopulationsofstar-forminggalaxiesatsimilarredshifts ( theLyman-Breakgalaxiesandthesub-mmselectedsources ) .Theinferreddensityoftheobjectsishigh,16 \pm 4perarcmin ^ { 2 } perunitredshift.ThisisconsistentwiththeintegratedluminosityfunctionforLyman-BreakgalaxiesdowntoR=27ifthefractionofLy \alpha emittinggalaxiesis \approx 70 % atthefaintendoftheluminosityfunction.However , ifthisfractionis20 % asreportedforthebrightendoftheluminosityfunctionthenthespacedensityinthisfieldissignificantlylarger ( byafactorof3.5 ) thanexpectedfromtheluminosityfunctionforLyman-BreakgalaxiesintheHDF–North.ThiswouldbeanindicationthatatleastsomeradioquietQSOsathighredshiftresideinoverdenseenvironmentsorthatthefaintendslopeofthehighredshiftluminosityfunctionhasbeenunderestimated.WefindevidencethatthefaintLy \alpha galaxiesareessentiallydust–free.TheseobservationsshowthatLy \alpha emissionisanefficientmethodbywhichtoprobethefaintendoftheluminosityfunctionathighredshifts .