Well, first thing’s first, you may want to dispel the notion that any of the folklore surrounding chandelure is true. That may be the source of your girlfriend’s trepidation. In as gentle and polite a manner as possible, remind her that you’re perfectly fine, even though you spend the most time around your chandelure than any human. Likewise, educate her (again, in a gentle, encouraging manner) about chandelure and how safe tamed ones can be.
If, however, her source of anxiety about your chandelure is not caused by popular folklore, consider asking her (politely) why she feels uncomfortable. Perhaps there are reasons you can address individually, and either way, listening to her can only improve your relationship.
Also, consider why you like your chandelure and highlight those reasons when describing it to your girlfriend. Illustrate through demonstrations (for example, if you consider your chandelure gentle, show your girlfriend how gentle it can be by allowing it to interact with your other pokémon) so she might begin to understand what your pokémon is like.
Finally, introduce your chandelure to her gradually. Consider including it in some of your activities (while keeping a close eye on it, of course) and work your way up to the point where your girlfriend may be able to interact with it directly.
In short, convincing a human being that a pokémon means no harm tends to be a gradual, complicated process that requires a level of effort on your part, but if you take things slow and do your best to portray your chandelure as the friendly, nonthreatening pokémon it surely is, your girlfriend may come around. It will just take a lot of patience for that to happen.
Best of luck, anonymous!