The polarizations of the Upsilon(1S), Upsilon(2S), and Upsilon(3S) mesons are measured as a function of the charged particle multiplicity in proton-proton collisions at root 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 4.9fb(-1). The results are extracted from the dimuon decay angular distributions, in two ranges of Upsilon(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 Upsilon(2S) and Upsilon(3S) cases. (C) 2016 The Author(s). Published by Elsevier B.V.