The rheology of blends of linear and branched poly(lactic acid) (PLA) architectures is comprehensively investigated. Measurement of the melt rheological properties of PLA is complicated by degradation effects but the addition of 0.35 wt% tris(nonylphenyl) phosphite (TNPP) provides excellent stabilization over a range of temperatures. Master curves of dynamic viscosity constructed using time-temperature superposition show significant dispersion for unstabilized samples; this behavior is accompanied by a loss of molecular weight. TNPP stabilized samples show excellent superposition throughout the entire frequency range and minimal loss in molecular weight. For the linear architecture, the Cox-Merz rule is valid for a large range of shear rates and frequencies. The branched architecture deviates from the Cox-Merz equality and blends show intermediate behavior. Both the zero shear viscosity and the elasticity (as measured by the recoverable shear compliance) increase with increasing branched content. The viscosities of both the unstabilized samples and the TNPP stabilized samples roughly obey a log additivity mixing rule. The recoverable shear compliance is monotonic in blend composition and a mixing rule for this property is also presented. For the linear chain, the compliance is independent of temperature but this behavior is apparently lost for the branched and blended materials. Tensile and thermal properties of the blends are also measured and found to be roughly equal within the statistical error of the experiments. The results suggest that excellent control over rheological behavior of PLA is possible through blending chain architectures without compromising mechanical properties.