The opening night in Los Angeles is Nov. 5, following previews from Oct. 28.
Richard Seyd directs the new play by Schenkkan, who won the Pulitzer Prize for Drama for The Kentucky Cycle.
Bichir, who is currently starring as Mary Louise-Parker's love interest on Showtime's "Weeds," will play Arturo, "a Cuban immigrant who is hired to (coincidentally) weed the garden of unconventional Austin widow Catherine," according to Geffen.
Obie Award winner Cochran, who will star as Catherine, comes straight from Chicago where she starred in The Lion in Winter at the Writers Theatre.
Bichir comes from one of the most well-known theatrical families in Mexico. On screen Bichir recently portrayed Fidel Castro in Steven Soderbergh's Che Guevara biopics "The Argentine" and "Guerilla." In his home country, Bichir's film "Sexo, Pudor y Lágrimas" held the box office record for number one movie in Mexico for three years straight, and he has been awarded numerous honors ranging from the prestigious Ariel Award for Best Actor to a medal presented by the cultural commission in Mexico City for distinction in the arts. Cochran has won acclaim for her work on some of America's most prominent stages including Steppenwolf, The Goodman and South Coast Repertory. She starred Off-Broadway in Bug, for which she was the recipient of the 2004 Theatre World Award, an Obie Award and was nominated for a Drama Desk Award.
Playwright Schenkkan said in production notes, "With this play, I'm doing something very different — a two-character contemporary love story. This kind of piece can be very challenging but in Demián and Shannon we have found two extraordinary talents who will bring out all of the complexity and passion with which these characters struggle. It's a great pleasure to bring this play to Los Angeles. Audiences here are so enthusiastic, sophisticated, and knowledgeable. With Babylon, I think they're in for a very special experience."
Performances continue on the Geffen mainstage to Dec. 7.
The creative team includes scenic designer Michael Ganio, lighting designer York Kennedy, sound designer Jon Gottlieb, costume designer Frances Kenny, projection designer Jason H. Thompson, production stage manager Mary Michele Miner and assistant stage manager Elizabeth A. Brohm.
For tickets visit GeffenPlayhouse.com or call (310) 208-5454 or Ticketmaster at (213) 365-3500.
Student rush tickets are available one hour prior to curtain for $15.
Geffen Playhouse is located at 10886 Le Conte Avenue, Westwood Village Los Angeles, CA.