Biodegradable polymers have significant potential in biotechnology and bioengineering. However, for some applications, they are limited by their inferior mechanical properties and unsatisfactory compatibility with cells and tissues. A strong, biodegradable, and biocompatible elastomer could be useful for fields such as tissue engineering, drug delivery, and in vivo sensing. We designed, synthesized, and characterized a tough biodegradable elastomer from biocompatible monomers. This elastomer forms a covalently crosslinked, three-dimensional network of random coils with hydroxyl groups attached to its backbone. Both crosslinking and the hydrogen-bonding interactions between the hydroxyl groups likely contribute to the unique properties of the elastomer. In vitro and in vivo studies show that the polymer has good biocompatibility. Polymer implants under animal skin are absorbed completely within 60 days with restoration of the implantation sites to their normal architecture.