Atomic force microscopy contact forces are shown to obey a Poisson distribution, so that the ratio of their variance to mean gives the force of a single chemical bond between the tip and sample. The derived single-bond force was able to distinguish nominal van der Waals interactions (60 +/- 3 pN) from hydrogen-bond interactions (181 +/- 35 pN) between atomic force microscope tips and gold and mica surfaces, respectively. This technique greatly reduced sampling time and sample wear, allowed quantitative use of low-resolution force data from a commercially available instrument, and detected important chemical differences between surface functional groups on the samples. These experiments constitute an important step in obtaining chemically specific information in atomic force microscopy.