Cecil James (Big Jay) McNeely (born on April 29, 1927 in Los Angeles, California), is an American rhythm and blues tenor saxophonist.

McNeely is known for his intense playing and his energetic and acrobatic stage performances. For example, at a 1949 concert in the old Wrigley Field baseball stadium in Los Angeles he played while walking through the stands and then while crawling from home plate to first base on his back. At a performance at the Apollo Theater in New York City in 1999, at the age of 72, he jumped onto the stage from the audience and later, wearing fluorescent gloves, played a fluorescent saxophone while break dancing under ultraviolet light. In the early 1950s his ability to whip teenagers into a frenzy was so disturbing to civic authorities in Los Angeles that he was banned from playing in most of Los Angeles county.

He was foremost among honking saxophonists – that is, saxophonists who played solos featuring squealing in the highest register while performing acrobatic and dance moves. He did not invent this style, but became its most famous practitioner. His performances were widely copied by early white rock and rollers. His most successful record, though, was a slow blues, "There is Something on Your Mind," with a vocal by Little Sonny Warner.

McNeely was inspired by Illinois Jacquet and by his teacher, Jack McVea. In 1947 he visited Johnny Otis's Barrelhouse Club in Los Angeles and was impressed by the energetic showmanship displayed by the performers there. Shortly after he performed on Otis's "Barrelhouse Stomp." Ralph Bass , a friend of Otis's, produced McNeely's first record for Savoy Records; Savoy issued it as by Big Jay McNeely because Cecil McNeely was not considered to be a commercial enough name. His first hit was "The Deacon's Hop" in 1949, which was followed by another hit, "Wild Wig." McNeely remained popular through the 1950s, but in the 1960s honking saxophone fell out of favour and McNeely quit the music business in 1971 to become a postman. However, he left the post office in 1983 and returned to touring and recording (for his own label).