Single-frequency diode lasers have been frequency stabilized to 1.5 kHz Allan deviation over 0.05-50 s integration times, with laser frequency drift reduced to less than 1.4 kHz/min, using the frequency reference provided by an ultranarrow inhomogeneously broadened Er3+:4I15/2?4I13/2 optical absorption transition at a vacuum wavelength of 1530.40 nm in a low-strain LiYF4 crystal. The 130 MHz full-width at half-maximum (FWHM) inhomogeneous line width of this reference transition is the narrowest reported for a solid at 1.5 孮 Strain-induced inhomogeneous broadening was reduced by using the single isotope 7Li and by the very similar radii of Er3+ and the Y3+ ions for which it substitutes. To show the practicability of cryogen-free cooling, this laser stability was obtained with the reference crystal at 5 K; moreover, this performance did not require vibrational isolation of either the laser or crystal frequency reference. Stabilization is feasible up to T=25 K where the Er3+ absorption thermally broadens to 500 MHz. This stabilized laser system provides a tool for interferometry, high-resolution spectroscopy, real-time optical signal processing based on spatial spectral holography and accumulated photon echoes, secondary frequency standards, and other applications such as quantum information science requiring narrow-band light sources or coherent detection.