The Broadway star had played matchmaking widow Dolly Levi on the stage, but Streisand won the title role in the 1969 big screen version of the musical.
And Channing admits she was so crushed, she considered jumping off her hotel balcony to end her "terrible pain".
She tells Dot429.com: "I was looking out the window on the 18th floor of the (hotel)... I thought, just one more move... and this terrible pain will stop, this pain of losing it for all time, they're all forgotten performances, it will stop, the moment that I hit, jumping out the window. That's exactly what I wanted to do."
And the 91 year old admits the only reason she decided against suicide was because she was due to appear onstage later that day.
She recalls, "I had a show that night to do, a matinee, as a matter of fact, that day. So I had to get ready for it."