The magnetic susceptibility and magnetization of high-quality single-crystal beta-TeVO4 are reported. We show that this compound, made of weakly coupled infinite chains of VO5 pyramids sharing corners, behaves as an S = 1/2 one-dimensional Heisenberg antiferromagnet. From magnetic experiments, we deduce the intrachain antiferromagnetic coupling constant, J/k(B) = 21.4 +/- 0.2 K. Below 5 K, a series of three phase transitions at 2.26, 3.28, and 4.65 K is observed.