The synthesis of hyperbranched poly(ethylene glycol) (hbPEG) in one step was realized by random copolymerization of ethylene oxide and glycidol, leading to a biocompatible, amorphous material with multiple hydroxyl functionalities. A series of copolymers with moderate polydispersity ((M) over bar (w)/(M) over bar (n) < 1.8) was obtained with varying glycidol content (3-40 mol-%) and molecular weights up to 49 800 g mol(-1). The randomly branched structure of the copolymers was confirmed by H-1 and C-13 NMR spectroscopy and thermal analysis (differential scanning calorimetry). MTS assay demonstrated low cell toxicity of the hyperbranched PEG, comparable to the highly established linear PEG.