Solid-state NMR observations of low-gamma half-integer quadrupolar nuclei, 35Cl and 37Cl, were demonstrated using a 24 T hybrid magnet (1H resonance frequency of 1.02 GHz) comprised of the high-temperature (HTS) and low-temperature (LTS) superconductors, and compared with results using a 14.1 T standard NMR magnet. While at 24 T the linewidth is 1.7 times narrower than that at 14.1 T, the gain in the sensitivity is 7.0 times because of enhanced polarization, reduced linewidth, and the use of larger rotor. A simple theoretical model was used to rationalize the sensitivity enhancements. The ratio of 35Cl and 37Cl quadrupolar couplings agrees well with the ratio of quadrupolar moments, and no isotope-dependent chemical shift has been observed. In addition, the 3QMAS spectrum of 35Cl is shown to demonstrate the high sensitivity rendered by the 24 T spectrometer.