We report the synthesis and shear rheology of a series of hydrogels derived from poly(vinyl acetate-b-vinyl alcohol-b-vinyl acetate) (PVAc-b-PVOH-b-PVAc) triblock copolymers. Bidirectional, reversible-addition fragmentation chain transfer free radical polymerizations of vinyl acetate (VAc) and vinyl chloroacetate (VC1Ac) are optimized to produce a series of relatively narrow dispersity PVAc-b-P(VAc-ran-VC1Ac)-b-PVAc triblock copolymers with controlled molecular weights and compositions. Rapid and selective hydrolysis of P(VAc-ran-VC1Ac) blocks with K2CO3/CH3OH furnishes access to a series of PVAc-b-PVOH-b-PVAc amphiphiles. Hydration of solvent-cast films of these copolymers, comprising PVAc blocks of comparable degrees of polymerization with variable PVOH segment lengths, yields soft hydrogels (G'(omega) similar to 1-10 kPa). Synchrotron small-angle and wide-angle X-ray scattering reveals that these hydrogels microphase separate into spherical hydrophobic PVAc domains that are interconnected by solvated PVOH network strands. The strain-dependent rheology of these hydrogels depends sensitively on the length of the center PVOH segment. This gel rheology is shown to stem from the hydrogen bond donor acceptor capabilities of PVOH, which leads to the formation of weak, dynamic noncovalent crosslinks in the aqueous domains of these gels. Thus, the observed gel rheology may be rationalized in terms of the shear-induced reorganization of these H-bonding crosslinks as a function of the applied strain.