We examine the possibility that very massive stars greatly exceeding the commonly adopted stellar mass limit of 150M ⊙ may be present in young star clusters in the local universe. We identify ten candidate clusters, some of which may host stars with masses up to 600M ⊙ formed via runaway collisions. We estimate the probabilities of these very massive stars being in eclipsing binaries to be 30%. Although most of these systems cannot be resolved at present, their transits can be detected at distances of 3 Mpc even under the contamination of the background cluster light, due to the large associated luminosities ∼ 10 7 L ⊙ and mean transit depths of ∼ 10 6 L ⊙ . Discovery of very massive eclipsing binaries would flag possible progenitors of pair-instability supernovae and intermediate-mass black holes.