Poly(lactic acids) (PLAs) are a family of polyesters available via fermentation from renewable resources and are the subject of considerable recent commercial attention. In this study, the melt rheological properties of a family of poly(lactic acid) stars are investigated and compared to the properties of the linear material. For polymers made from a 98:2 ratio of the L to D enantiomeric monomers it is found that the entanglement molecular weight is in the range of 9000 g per mole (M-e approximate to 8700 g/mol) while the molecular weight for branch entanglement is inferred to be approximately 3500 g per mole (M-b approximate to 34 600 g/mol). In addition, the zero shear viscosity of the linear material increases with the 4.6 power of molecular weight. These results may suggest that PLA is a semistiff polymer in accordance with other recent findings. The increase in zero shear viscosity for the branched materials is measured and quantified in terms of appropriate enhancement factors. Relaxation spectra show that the transition zone for the linear and branched materials an nearly indistinguishable, while the star polymers have greater contributions to the terminal regime. The effects of chain architecture on the flow activation are found to be modest, implying that small scale motions in PLA homopolymers largely control this phenomenon. Good agreement is found between the dynamic data and many aspects of the theory of star polymers, however, a dependence of the zero shear viscosity on the number of arms is observed.