A hyperbranched aliphatic polyester has been functionalized with PEG chains to afford a novel water‐soluble BH40‐PEG polymer which exhibits unimolecular micellar properties, and is therefore appropriate for application as a drug‐delivery system. The solubility of the anticancer drug paclitaxel was enhanced by a factor of 35, 110, 230, and 355 in aqueous solutions of BH40‐PEG of 10, 30, 60, and 90 mg · mL⁻¹, respectively. More than 50% of the drug is released at a steady rate and release is almost complete within 10 h. The toxicity of BH40‐PEG was assessed in vitro with A549 human lung carcinoma cells and found to be nontoxic for 3 h incubation up to a 1.75 mg · mL⁻¹ concentration while LD₅₀ was 3.5 mg · mL⁻¹. Finally, it was efficiently internalized in cells, primarily in the absence of foetal bovine serum, while confocal microscopy revealed the preferential localization of the compound in cell nuclei.