The ALICE experiment at the LHC has studied inclusive J/ production at central and forward rapidities in pp collisions at TeV. In this Letter, we report on the first results obtained detecting the J/ through its dilepton decay into and pairs in the rapidity range |y|<0.9 and 2.5<y<4, respectively, and with acceptance down to zero . In the dielectron channel the analysis was carried out on a data sample corresponding to an integrated luminosity = 5.6 nb and the number of signal events is (stat.) 28 (syst.); the corresponding figures in the dimuon channel are = 15.6 nb and (stat.) 144(syst.). The measured production cross sections are (|y|<0.9) = 12.4 1.1 (stat.) 1.8 (syst.) + 1.8 -2.7 (syst.pol.) b and (2.5<y<4) = 6.31 0.25 (stat.) 0.76 (syst.) +0.95 -1.96 (syst.pol.) b. The differential cross sections, in transverse momentum and rapidity, of the J/ were also measured.