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The ALICE Collaboration reports the measurement of the relative J/psi yield as a function of charged particle pseudorapidity density dN(ch)/d eta in pp collisions at root s = 7 TeV at the LHC. J/psi particles are detected for p(t) > 0, in the rapidity interval vertical bar y vertical bar < 0.9 via decay into e(+)e(-), and in the interval 2.5 < y < 4.0 via decay into mu(+)/mu(-) pairs. An approximately linear increase of the J/psi yields normalized to their event average (dN(J/psi)/dy)/(dN(J/psi)/dy) with (dN(ch)/c eta)/(dN(ch)/d eta) is observed in both rapidity ranges, where dN(ch)/d eta is measured within vertical bar eta vertical bar < 1 and p(t) > 0. In the highest multiplicity interval with (dN(ch)/d eta)(bin)) = 24.1, corresponding to four times the minimum bias multiplicity density, an enhancement relative to the minimum bias J/psi yield by a factor of about 5 at 2.5 < y <4 (8 at vertical bar y vertical bar < 0.9) is observed. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.