Never mind the elephant in the room. It’s impossible to ignore the elephant in this word.
But wait. Let’s look at the rest first. What’s this chrys? Does Chrysler leap to mind? You may think this is an adjective for a Chrysler 300C, or perhaps a Town & Country. Huge, padded vehicles. But chryselephantine is not related to Chrysler (which is actually an old Dutch name), and it’s not pronounced the same way either. Our chrys of the day is said “kris,” the same as in chrysalis and chrysotile. And it means the same thing.
What thing is that? Gold. Greek χρῡσός chrusos. So is this a word for a golden elephant? Not so much the whole elephant. What have elephants been most valued for? I don’t mean their intelligence, loyalty, and work ethic – I’m talking about what thing has gotten them killed most often so people could steal it from them. Yes, ivory. The Greek word for ‘elephant’, ἐλέϕας elefas, is the same as the Greek word for ‘ivory’, and there’s an obvious reason for that.
So there we have it. Gold and ivory. And the ine? Just an adjectival ending. It doesn’t mean it’s a mineral or someone’s name (although that would be a heck of a name to have). It’s pronounced like “in.” The whole word is said /krɪsɛlɪˈfæntɪn/.
So a thing that is chryselephantine is… no, not made of gold and ivory, not generally. Just inlaid or overlaid with them. I mean, come on. That stuff is expensive. And, actually, in one of the two cases, illegal now for new production (I mean theft from its now-dead producers).
So you won’t be using this word much literally unless you deal in expensive antiques and antiquities. But you can still use it figuratively, especially if you want to be opaquely precious. Prose, verse, or music that is shining, gleaming, very valuable, can earn this sobriquet in high approbation. It’s sort of like throwing an overpriced statue at it. It’s a heavy word, so old, so expensive. It will drive the avid reader to the dictionary and the less avid reader to lighter reading. But it’s a word to keep in your collection. Just be careful who you show it to.