In her memoir Just Lucky I Guess (2002), Channing revealed that in 1937, when she was a 16-year-old about to head off to Bennington College, her mother told her that her father's birth certificate had marked him as "colored," as his mother had been black. It was an unexpected revelation for Channing, and she didn't make the information public for decades (a decision that allowed her to avoid the discriminatory treatment African Americans faced at the time).
Her father, born in Augusta, Georgia chose to pass for white and was born with the last name Stucker which he changed to Channing before Carol was born. Her mother told her of her roots so that she wouldn't be surprised if she had a black baby.
Source: African American Registry