Christmas Island (クリスマス島 Kurisumasu tō?) is the place where Sonic the Hedgehog was born, according to the Japanese backstory from the Sonic the Hedgehog Technical Files. No other information is known or ever given about this island nor it has ever referred to in game appearances or any other media, but it appears to be based on one of several real-life islands of the same name.
The translation for the backstory was made by Sega Technical Institute for History Book, that has been featured as part of the limited Birthday Pack of Sonic Adventure 2 during Sonic's tenth anniversary.
- Sonic Dimension - With original Japanese translation of the backstory (courtesy of archive.org)