We report on the molecular beam epitaxy growth of modulation-doped GaAs-(Ga,Al)As heterostructures on the (311)A GaAs surface using silicon as the acceptor. Two-dimensional hole gases (2DHGs) with low-temperature hole mobility exceeding 1.2 x 10(6) cm(2) V-1 s(-1) with carrier concentrations as low as 0.8 x 10(11) cm(-2) have been obtained. This hole mobility is the highest ever observed at such low densities by any growth technique. We also report the first observation of persistent photoconductivity in a 2DHG. An analysis of the number density and temperature dependence of the mobility leads us to conclude that the mobility is limited by phonon scattering above similar to 4 K and interface scattering at lower temperatures.