I posted this on our affiliated forum, but I would like as much involvement as possible.
I've done extensive research through news articles and scans but have never found an exact date stated anywhere. I calculated an approximate date of December 8th based off "The Chipmunk Song" (their first official vocal performance and official creation). This date came from a Billboard article released December 15th, 1958 stating clearly that the record topped nearly every store's sales. Furthermore, that same article stated "even this disk didn't catch hold until about a week ago." The song hit number one on December 22nd. So, without a doubt, any date after the 22nd can be thrown out along with those between the 15th and 22nd.
Going back further I noticed that in the December 8th, 1958 Billboard article it's stated "Seville has gotten back on the winning track with his new hit record of 'The Chipmunk Song.'" This would imply that even December 8th, 1958 (the long accepted provable birthday to me) isn't correct either as the record is selling well, but not as good as by the 15th and the 22nd.
Continuing back I looked closer. In the December 1st Billboard article I noticed something new that I missed in the past - the song is currently #62 on the Hot 100 chart and is the song's first time on this chart. Some jocks were playing the track "ahead of schedule." Was the track not supposed to have been released before Thanksgiving?
The track is out in the November 24th Billboard article as a distribution company calls it the "strongest new record" while some jocks were playing the track before Thanksgiving and/or labeled it the "Pick Hit of the Week" (week of Nov. 16th) or the "biggest Christmas novelty this year."
November 7th is the earliest cap based off when Ross Sr completed writing the song. He later took it to a small Minneapolis station, but that date isn't known. (Web Archive) Plus, there's no indication of when sales actually started.
Based off the additional information I've found, December 8th isn't correct or acceptable. If you know anything in addition to what's been posted, please share (don't forget a link to the source). Let's see if we can finally solve this mystery.
Been looking further, I discovered a blog claiming the song was released November 19th. No source though so I researched the date more. Led to a book, which, unfortunately, I can't assess. Based off the snippet Google provided, this book knows the week the track was released.
Switching gears, I started looking at the record itself. Looking at the catalog number, F-55169, I found Nov. 18th, 1958. I then looked at the Monarch (the manufacture of the records) △ (Delta) numbers, which give an idea of when the records were pressed, and found they were pressed before mid-Nov. No big help there. So, it looks like we might be narrowed down to three dates: Nov 17th, 18th, and 19th.