There are several place in the world called "Christmas Island". Since the song is about a tropical escape from snow and cold, some of them can be ruled out as the one referred to herein. On that can be ruled out is a Christmas Island in the Canadian province of Nova Scotia. It would not fit at all the warm tropical mood of the song; it would tend to be frigid around Christmas. There are also two Christmas Islands in Australia. One is in the State of Tasmania. It could be comfortable and snow-free there at Christmas, since Christmas comes in the Southern Hemisphere's summer. Still, the song's reference to coconut trees would pretty much rule out that Christmas Island, as it doesn't have a year-round warm climate. The other Australian Christmas Island is a territory in the Indian Ocean. It has a tropical climate, but is not the best known place to ever be called Christmas Island. So the place most likely referred to in the song is the best known place to ever have that name, an island in the now-independent nation of Kiribati, in the southern Pacific Ocean. That island's long standing name of Christmas Island reflects its British past, as it was part of the British protectorate and then colony of Gilbert And Ellice Islands from 1982 to 1976. Thereafter the Gilbert Islands became independent as Kiribati, which contains the island with the official name Kiritimati, still widely remembered as "Christmas Island". Incidently, the name "Kiritimati" sounds somewhat more like "Christmas" than the spelling might lead many to believe.