who was the first artist to release a "greatest hits" compilation

The first "Greatest Hits" compilation was by Johnny Mathis. "Johnny's
Greatest Hits" was released by Columbia in 1958.

"Johnny Mathis's Johnny's Greatest Hits (1958) is generally considered
the first greatest-hits album. It sold well, remaining on the
Billboard Top Albums Chart for a then-recordbreaking 490 continuous
weeks."

Wikipedia: Greatest hits
http://en.wikipedia.org/wiki/Greatest_hits

"Back in 1956 recording artist Johnny Mathis was forced to make the
decision between trying out for the United States Olympic team (his
specialty was track) or recording his first album for Columbia
Records. He chose the latter and went on to become the eighth biggest
selling album artist of all time. His 1958 album, Johnny's Greatest
Hits, was the first Greatest Hits album ever marketed, spending three
weeks at #1 and 490 consecutive weeks on Billboard's Pop Album chart
(that's almost 9 ½ years!)."

BillyBearTrivia: Some Interesting Facts
http://launch.groups.yahoo.com/group/billybeartrivia/message/102427

"Johnny's accomplishments are numerous and varied. He holds many
records and has set many precedents in the music industry. In 1958,
two years after being signed by Columbia Records, Johnny's 'Greatest
Hits' was released. It began a 'Greatest Hits' tradition copied by
every record company since then."

Richard De La Font Agency: Johnny Mathis
http://www.delafont.com/music_acts/johnny-mathis.htm

"In 1958 Mathis moved his center of operations to Los Angeles, where
he has continued to reside ever since. A 'Greatest Hits' collection
(the first time a record had been titled as such) was released by
Columbia that same year, subsequently setting a new industry record by
remaining on the charts continuously for 490 weeks."

NNDB: Johnny Mathis
http://www.nndb.com/people/869/000023800/

My Google search strategy:

Google Web Search: "first greatest hits album"
://www.google.com/search?hl=en&q=%22first+greatest+hits+album%22

Google Web Search: "the first greatest hits" "johnny mathis"
://www.google.com/search?hl=en&q=%22the+first+greatest+hits%22+%22johnny+mathis%22

I hope this is helpful. If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

so good that I feel stupid for not being able to find it myself

Thank you very much for the five stars and the generous tip!

~pinkfreud