The polarizations of the ϒ(1S) , ϒ(2S) , and ϒ(3S) mesons are measured as a function of the charged particle multiplicity in proton–proton collisions at s=7 TeV . The measurements are performed with a dimuon data sample collected in 2011 by the CMS experiment, corresponding to an integrated luminosity of 4.9 fb −1 . The results are extracted from the dimuon decay angular distributions, in two ranges of ϒ(nS) transverse momentum (10–15 and 15–35 GeV), and in the rapidity interval |y|<1.2 . The results do not show significant changes from low- to high-multiplicity pp collisions, although large uncertainties preclude definite statements in the ϒ(2S) and ϒ(3S) cases.