A tris[3-(alkoxysilyl)propyl] isocyanurate from the group of tris[3-(trialkoxysilyl)propyl] isocyanurate, tris[3-(alkyldialkoxysilyl)propyl] isocyanurate and tris[3-(dialkylalkoxysilyl)propyl] isocyanurate is prepared by hydrosilylation, by a) initially charging a mixture of at least one hydroalkoxysilane from the group of hydrotrialkoxysilane, hydroalkyldialkoxysilane, hydrodialkylalkoxysilane [called H-silane(s) for short] and a Pt catalyst, b) heating the mixture to a temperature of 40 to 170° C., c) then adding or metering in 1,3,5-triallyl-1,3,5-triazine-2,4,6(1H,3H,5H)-trione, at least one carboxylic acid and at least one alcohol as cocatalyst while mixing, and d) leaving the mixture to react and then working up the product mixture thus obtained.