We show that spin S Heisenberg spin chains with an additional three-body interaction of the form (Si-1 center dot S-i)(S-i center dot S-i (+) (1)) + H.c. possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to 1/[4S(S + 1) - 2]. This result generalizes the Majumdar-Ghosh point of the J(1) - J(2) chain, to which the present model reduces for S = 1/2. For S = 1, we use the density matrix renormalization group method to show that the transition between the Haldane and the dimerized phases is continuous with a central charge c = 3/2. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.