"One for My Baby" is a popular song written by Harold Arlen

Harold Arlen

Harold Arlen was an American composer of popular music, having written over 500 songs, a number of which have become known the world over. In addition to composing the songs for The Wizard of Oz, including the classic 1938 song, "Over the Rainbow,” Arlen is a highly regarded contributor to the...

 and Johnny Mercer

Johnny Mercer

John Herndon "Johnny" Mercer was an American lyricist, songwriter and singer. He is best known as a lyricist, but he also composed music. He was also a popular singer who recorded his own songs as well as those written by others...

 for the musical The Sky's the Limit (1943) and first performed in the film by Fred Astaire

Fred Astaire

Fred Astaire was an American film and Broadway stage dancer, choreographer, singer and actor. His stage and subsequent film career spanned a total of 76 years, during which he made 31 musical films. He was named the fifth Greatest Male Star of All Time by the American Film Institute...

. It was popularized by the American

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 singer Frank Sinatra

Frank Sinatra

Francis Albert "Frank" Sinatra was an American singer and actor.Beginning his musical career in the swing era with Harry James and Tommy Dorsey, Sinatra became an unprecedentedly successful solo artist in the early to mid-1940s, after being signed to Columbia Records in 1943. Being the idol of the...

. "One for My Baby" is the theme song of the 1957-1958 NBC

NBC

The National Broadcasting Company is an American commercial broadcasting television network and former radio network headquartered in the GE Building in New York City's Rockefeller Center with additional major offices near Los Angeles and in Chicago...

 detective

Detective

A detective is an investigator, either a member of a police agency or a private person. The latter may be known as private investigators or "private eyes"...

 series, Meet McGraw

Meet McGraw

Meet McGraw is an American dramatic television series starring Frank Lovejoy in the role of the hard-hitting detective McGraw, a man specifically given no first name in the program. Forty-one half-hour episodes aired on NBC during the 1957-1958 season, sponsored by Procter & Gamble. The series was...

, starring Frank Lovejoy

Frank Lovejoy

Frank Lovejoy was an American actor in radio, film, and television. He was born Frank Lovejoy Jr. in Bronx, New York, but grew up in New Jersey. His father, Frank Lovejoy Sr., was a furniture salesman from Maine...

.

Harold Arlen described the song as "another typical Arlen tapeworm" - a "tapeworm" being the trade slang for any song which went over the conventional 32 bar length.