We have used n→ 1 1 1 In→ 1 1 1 Cd perturbed-angular-correlation (PAC) spectroscopy to measure hyperfine interactions at surface sites on GaAs(111)B (As-terminated) surfaces. The (111)B surfaces form two reconstructions, 2 2, which is formed under As-rich conditions and is stable below ∼700 K, and √19 √19R23.4°, which is formed under Ga-rich conditions above this temperature. These nearly-atomically-flat surfaces were grown using molecular beam epitaxy. During each experiment, the n 1 1 1 In probe atoms were effused onto the GaAs surface, and a series of thermal anneals was performed. A laboratory-temperature PAC measurement was made after each anneal. The PAC measurements performed on the 2 2 reconstructed surfaces show two well-defined nuclear electric-quadrupole interactions that occur at two inequivalent Ga-sites on the surface. The corresponding electric-field gradients (EFGs) are large and asymmetric: V z z 8.6 10 1 7 V cm - 2 , and η 0.47 and V z z 16.5 10 1 7 V cm - 2 and η 0.85; the respective site fractions are ∼50% and ∼30%. The measurements performed on the √19 √19R23.4° reconstructed surfaces show one well-defined interaction that involved ∼82% of the probes. The corresponding EFG is also large and asymmetric: V z z 16.7 10 1 7 V cm - 2 and η 0.8, and the EFG z-axis is oriented essentially perpendicular to the surface. Annealing experiments were performed to convert one reconstruction to the other and then to reconvert it back to the original reconstruction, e.g., 2 2→√19 √19R23.4°→2 2. The PAC measurements that followed each annealing step show the characteristic frequencies for each reconstruction. This result indicates that these probe sites are thermodynamically stable. Additionally, at high annealing temperatures and during these thermal-cycling experiments, a small fraction of the probes appear to diffuse into the bulk crystal. The interpretation of the probe-site assignments does not agree with a model of the √19 √19R23.4° reconstructed surface developed using scanning tunneling microscopy. These experiments represent the first measurements of group III bonding symmetries on a compound III-V semiconductor surface. The corresponding analysis indicates that these symmetries differ qualitatively from the conventional picture.