Poly(lactic-co-glycolic acid) (PLGA) is a biodegradable copolymer that is also acceptable for use in a variety of biomedical applications. Typically, a random PLGA polymer is synthesized in a bulk batch polymerization using a tin-based catalyst at high temperatures. This methodology results in relatively broad polydispersity indexes (PDIs) due to transesterification, and the polymer product is often discolored. We report here the use of 1,8-diazabicyclo[5.4.0] undec-7-ene (DBU), a known, effective, and convenient organocatalyst for the ring-opening polymerization of cyclic esters, to synthesize random copolymers of lactide and glycolide. The polymerization kinetics of the homo- and copolymerizations of lactide and glycolide were explored via NMR spectroscopy. A novel strategy that employs a controlled addition of the more reactive glycolide monomer to a solution containing the lactide monomer, the poly(ethylene glycol) (PEG) macroinitiator, and DBU catalyst was developed. Using this tactic (semibatch polymerization), we synthesized a series of block copolymers that exhibited excellent correlation of the expected and observed molecular weights and possessed narrow PDIs. We also measured the thermal properties of these block copolymers and observed trends based on the composition of the block copolymer. We also explored the need for experimental rigor in several aspects of the preparations and have identified a set of convenient reaction conditions that provide polymer products that retain the aforementioned desirable characteristics. These polymerizations proceed rapidly at room temperature and without the need for tin-based catalysts to provide PEG-b-PLGAs suitable for use in biomedical investigations.