In “The Visit,” Claire returns to the town of her birth in what seems to be a bid to restore it to prosperity as well as to reclaim Anton, the lover who once wronged her. The catch? Before the largess flows, she wants Anton dead. In his postscript to the play, Dürrenmatt, who has a way with understatement, called it a “a somewhat distressing love story.”

Offstage, Ms. Rivera didn’t seem quite so vengeful, no matter how much black eyeliner she wore (a lot), as she chatted and sipped a giant mug of Throat Coat tea. (“I don’t do honey,” she said. “I’m always thinking of my weight.”) The play’s director, John Doyle, described her in an interview before a performance as “a thoroughly good human being” and “a really fine person,” worlds away from the murderous Claire.

Ms. Rivera demurred. “Oh no,” she said in her purring voice. “I’m perfectly cast.”

Producers had originally approached Angela Lansbury about the role, but when Ms. Lansbury’s husband fell ill, Ms. Rivera stepped up, which is just a little harder for her than it used to be. In 1986, a car accident broke her left leg in 12 places. Sixteen metal screws now hold it in place, a condition that Ms. Rivera feels when she rushes down the Lyceum’s rickety backstage stairs, underneath the stage and up another flight, as she must for an entrance in the middle of the play.

Ms. Rivera apparently would have accepted the role no matter how many stairs it demanded. She has Kander and Ebb (John Kander is still living at 88, and Fred Ebb died in 2004) and the book writer Terrence McNally to thank for her two Tony awards, as Anna in “The Rink” and Aurora in “Spider Woman.” She would have starred in anything they devised, she says. “If they wrote about the phone book, I would have done it,” she said.