Bring water to a boil in a medium saucepan. Stir in sugar and cocoa; reduce heat, and simmer 5 minutes, stirring frequently. Remove from heat; add chocolate and vanilla, stirring until chocolate melts. Cover and chill completely.
Pour chocolate mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 1 hour or until firm.