I'm not aware of any laws. We were told in med school that for our own protections, guys must bring a chaperone in / women should consider it... but it's less likely and we didn't always.
Based on this research paper, studies are limited.
Legally, looks like it's not mandated in most states:
The AMA, the American Academy of Pediatrics, and the American Congress of Obstetricians and Gynecologists all state that a patient’s request for a chaperone should be honored, none of them require the use of chaperones, and only seven states require chaperones under some conditions