We report here the low-pressure metalorganic chemical vapor deposition growth of AlGaAs-GaAs quantum well heterostructures having low-temperature (4.2 K) photoluminescence spectra with full width at half-maximum (FWHM) values ranging from approximately 6 to 4 meV for quantum wells having 6-28 monolayer (ML) widths, respectively. These linewidths are compared to those measured for quantum wells grown by molecular beam epitaxy, flow-rate modulation epitaxy, and atomic layer epitaxy. We find that the FWHM values for the thinnest quantum wells grown in the present study (approximately 6 ML) are equal to or narrower than those observed for comparable structures produced by other technologies.