Two-dimensional electron gases (2DEGs) formed at the interface of insulating complex oxides promise the development of all-oxide electronic devices. These 2DEGs involve many-body interactions that give rise to a variety of physical phenomena such as superconductivity, magnetism, tunable metal-insulator transitions and phase separation. Increasing the mobility of the 2DEG, however, remains a major challenge. Here, we show that the electron mobility is enhanced by more than two orders of magnitude by inserting a single-unit-cell insulating layer of polar La1-xSrxMnO3 (x = 0, 1/8, and 1/3) at the interface between disordered LaAlO3 and crystalline SrTiO3 produced at room temperature. Resonant X-ray spectroscopy and transmission electron microscopy show that the manganite layer undergoes unambiguous electronic reconstruction, leading to modulation doping of such atomically engineered complex oxide heterointerfaces. At low temperatures, the modulation-doped 2DEG exhibits Shubnikov-de Haas oscillations and fingerprints of the quantum Hall effect, demonstrating unprecedented high mobility and low electron density.