Chance was born an engineer's son in Wilkes-Barre, Pennsylvania; he was educated at the University of Pennsylvania, where he obtained his PhD in 1940 and where he served as E. R. Johnson Professor of Biophysics from 1949 to 1983.

In 1943 he carried out a spectroscopic analysis that provided firm evidence for the enzyme–substrate complex whose existence had been confidently assumed by biochemists since the beginning of the century. Working with the iron-containing enzyme peroxidase, which strongly absorbs certain wavelengths of light, he found that variations in light absorption could be precisely correlated with rates of production of the enzyme–substrate complex. This was seen as confirming the important work of Leonor Michaelis.

Chance has also contributed to one of the great achievements of modern biochemistry, namely the unraveling of the complicated maze through which energy is released at the cellular level. He found that the concentration of ADP (adenosine diphosphate), as well as the oxygen concentration, determined the oxidation and reduction states of the proteins in the respiratory (electron-transport) chain. His studies of changes in ADP concentration led to a better understanding of how glucose is used in the body.