None of the electronic parts suppliers I tried carry any music chips at all.
This might be explained if you look on Ebay for "Doorbells". You can buy musical door bells with a wireless connection between the push button and the music player, for as little as $2.
If you really wanted the chip, I guess you could just take one out of one of these cheap door bells. But why would you bother if you just wanted to make a door bell anyway?
Just use the one from Ebay.
I should mention that the Picaxe 08M has 4 songs built into it and you can program new songs.
However you would need a programmer to do this.
Doorbells that play music are actually more embarassing than anything. They play a song, but the song may be inappropriate for the visitors and you may have to apologise for it.
A chiming one that just gives two sounds of different pitch is a lot more classy.