  We study the phase diagram of a one-dimensional version of the Kitaev
spin-1/2 model with an extra ``$\Gamma$-term", using analytical, density matrix
renormalization group and exact diagonalization methods. Two intriguing phases
are found. In the gapless phase, although the exact symmetry group of the
system is discrete, the low energy theory is described by an emergent SU(2)$_1$
Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation
functions exhibit SU(2) breaking prefactors, even though the exponents and the
logarithmic corrections are consistent with the SU(2)$_1$ predictions. A
modified nonabelian bosonization formula is proposed to capture such exotic
emergent ``partial" SU(2) symmetry. In the ordered phase, there is numerical
evidence for an $O_h\rightarrow D_4$ spontaneous symmetry breaking.
