Alexander was 92 and died less than two weeks after his married partner, Shaun O'Brien. O'Brien died Feb. 23 and Alexander died March 7 in the Saratoga Springs, N.Y., house they shared, The New York Times reported Saturday.
"If there is a cause of death, it's a broken heart," Alexander's friend Jane Klain said when confirming Alexander's death. "It's as simple as that."
Alexander was born Allen Smith Jan. 14, 1920, in Tulsa, Okla., but left in 1938 with high school chum Tony Randall.
"I came to New York because I thought they were waiting for me," Alexander once said.
He went to a psychic who told him to alter the spelling of his name.
"Well I can guarantee you success if you do one thing," Alexander quoted her as saying. "Call yourself 'Chris' and take the 'h out."
He landed the major part of "Chip" in the stage musical "On the Town" and did some summer stock, but he paid the bills as a photographer shooting portraits of stars, working with the New York City Ballet and Andy Warhol's Interview magazine, the Times said.
In 1961, Alexander shot pictures for "Little Me," which became a best-selling satire of a movie star's memoir that Neil Simon later adapted for the Broadway stage.
That shoot for "Little Me" was, as Charles Busch, writer of "Vampire Lesbians of Sodom" said, "a seminal moment in the popularization" of the camp movement.
Alexander left no immediate survivors and funeral arrangements were unclear.