We report rheological data on hydrogels formed from triblock copolymers of poly(L-lactide) (PLLA) and poly(ethylene oxide) (PEO). We are able to create gels with elastic moduli greater than 10,000 Pa, which is an order of magnitude higher than previously achieved with related physically associated gels of similar chemistry. Moreover, the value of the elastic modulus strongly depends on PLLA block length, offering a mechanism to control the mechanical properties as desired for particular applications. Additionally, we have developed protocols for using these materials for cell encapsulation and present preliminary cell viability studies for encapsulated human liver cells (HepG2 cell line). Our results have implications for the design of new materials for soft tissue engineering, where native tissues have moduli in the kPa range.