High-pressure atom transfer radical polymerization (ATRP) of n-butyl acrylate (BA) is performed in acetonitrile (MeCN) with CuIBr/TPMA [TPMA: tris(2-pyridylmethyl)-amine] as the catalyst up to 5 kbar. Increasing either pressure or temperature significantly enhances the rate of polymerization, while retaining control over the polymerization. The polymerizations under high pressure could be efficiently performed with very low levels of Cu catalyst in the absence of any reducing agents. For example, 100 ppm Cu is sufficient to catalyze the polymerization of BA with targeted degree of polymerization (DPT) = 1000. The conversion reached 79% in 3.0 h at 80 degrees C providing PBA with Mn = 112 000, Mw/Mn = 1.12. Since the initial CuI-to-initiator molar ratio is 0.05:1, the molar percentage of terminated chains should remain <5%. For DPT = 10 000 using only 50 ppm Cu catalyst, a polymer with molecular weight Mn = 612 000 (DP = 4800) was obtained at 67% conversion.