  We report on the first measurement of J/Psi production as a function of
charged particle pseudo-rapidity density dN_ch/d_eta in pp collisions at
sqrt{s} = 7 TeV with the ALICE experiment at the LHC. J/Psi mesons are detected
down to p_T = 0 via their decays into e+e- pairs at mid-rapidity (|y| < 0.9)
and into mu+mu- pairs at forward rapidity (2.5<y<4). dN_ch/d_eta is measured
within |eta| < 1. We compare results in the two different J/Psi rapidity
ranges. Preliminary PYTHIA simulations are also presented.
