First episode: July 2, 1953
    Bill's first episode: Jan 28, 1954
Last episode: September 13, 1955
Until Aug 26, 1954: Thurs at 10:30pm (CBS)
Sept 18 - Dec 25, 1954:  Sat at 8:30pm (NBC)
June 28 - Sept 13, 1955:  Tuesdays at 8:00pm (NBC)
Contestants were shown a face from their past (recent or distant) and tried to identify it with help from comical clues offered by the host.  Jack Smith was the original host, followed by Jack Bailey.  By the time Bill took over, most of the contestants were celebrities and interviews took up much of the show.

Despite being a show played mostly for laughs, the program ran a $25,000 contest -- huge for the time -- called "Three Face" starting in March, 1954.  Viewers sent in messages supporting the Heart Fund (in 25 words or less, of course), and the writers of some of those letters won the opportunity to identify the three faces that made up a composite picture.

On August 26, 1954 the show ended its CBS run.  The following week, Bill began hosting Name That Tune for the same sponsor (Toni) in the same time slot.  When NBC picked up Place the Face two weeks later at a different day and time, Bill hosted both shows.  Place the Face would be cancelled yet again two months later, only to reappear (with Bill) as a summer series in 1955.
Place the Face was based in Hollywood, requiring Bill to commute across the country once a week to host it.  Bill's announcer on Place The Face was Jack Narz.  Bill married the sister of Narz's wife, making the two game show veterans brothers-in-law.

One episode exists, with celebrity guest Xavier Cugat. 
Watch the surviving episode:  

Our thanks to Fredrick Tucker, who got us started on this with his own research into the career of Verna Felton.  Even though these shows probably don't exist anymore, it's still interesting to see some of the big names (and not so big names) who paid Bill a visit! 

January 21 No Data
June 28 Jeff Donnell, Aldo Ray, Gale Robbins
January 28 Sheree North, Andy Devine
July 5 June Havoc, Pedro Gonzales
February 4 No Data
July 12 No Data
February 11 No Data
July 19 Elyse Knox, Barbara Hale, Andy Devine
February 18 Brian Donlevy, Phil Harris, Verna Felton
July 26 Joan Bennett, George Liberace
February 25 Joan Bennett, Charles Farrell, Hal March
August 2 Bob Cummings, The Mills Brothers
March 4 Bob Crosby, Benny Rubin
August 9 Sammy Davis Jr, Mona Freeman 
March 11 No Data
August 16 Dick Powell, Helen O'Connell
March 18 No Data
August 23 No Data
March 25 No Data
August 30 Dorothy Lamour, Keefe Braselle
April 1 No Data
September 6 No Data
April 8 No Data
September 13 No Data
April 15 Clyde Beatty, Mickey Rooney

April 22 No Data

April 29 No Data

May 6 No Data

May 13 Dona Atwood

May 20 Sally Rand, Lord Blears, Jack Carson

May 27 No Data

The Place the Face page at Adam Nedeff's Bill Cullen's World
Theme music copyright information at David Shields' site for Classic TV Themes