Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (Si-1 . S-i)(S-i . Si+1) + H.c., we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S = 1, 3/2, and 2. The resulting central charge and critical exponent are in good agreement with the SU(2)(k=2S) Wess-Zumino-Witten values c = 3k/(2 + k) and eta = 3/(2 + k). Since the three-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU(2)(k>1) Wess-Zumino-Witten models might finally be realized in actual spin chains.