According to the report, the majority of Goodell's time was spent with him under cross-examination by union attorney Jeffrey Kessler. Rice and his wife Janay both attended the hearing, which will continue on Thursday.
ESPN reports that both Rice and his wife are expected to testify on Thursday, and NFL security chief Jeffrey Miller and Ravens president Dick Cass are also expected to testify over the two-day hearing.
Last month, it was reported that Goodell would be forced to testify at Rice's hearing, which is being heard by former U.S. district judge Barbara Jones as a neutral arbitrator.
Rice is appealing his indefinite suspension handed to him by Goodell on Sept. 8 following the release of footage showing Rice punching Janay -- then his fiancée -- in an Atlantic City casino elevator.
Goodell suspended Rice for two games over the summer after his arrest on domestic violence charges, and Rice is expected to argue that the commissioner had no basis to extend his suspension from two games to an indefinite period.
CBSSports.com's Jason La Canfora has said several legal experts told him Rice "has an exceedingly strong case." If his appeal is successful, he could theoretically return to the NFL this season.
The running back has also filed a grievance against the Ravens for terminating his contract just hours before the NFL gave him the indefinite suspension.
- Molly Geary