The first evidence of spin alignment of vector mesons (K 0 and ϕ) in heavy-ion collisions at the Large Hadron Collider (LHC) is reported. The spin density matrix element ρ00 is measured at midrapidity (jyj < 0.5) in Pb-Pb collisions at a center-of-mass energy ( ffiffiffiffiffiffiffi sNN p ) of 2.76 TeV with the ALICE detector. ρ00 values are found to be less than 1=3 (1=3 implies no spin alignment) at low transverse momentum (pT < 2 GeV=c) for K 0 and ϕ at a level of 3σ and 2σ, respectively. No significant spin alignment is observed for the K0 S meson (spin ¼ 0) in Pb-Pb collisions and for the vector mesons in pp collisions. The measured spin alignment is unexpectedly large but qualitatively consistent with the expectation from models which...