You can ask a jeweler, or you can try to fix it yourself. If you want to fix it yourself, make sure the broken edges match up, first of all, and wipe it down with alcohol to remove any oils left from your skin. You should use an epoxy, one that dries clear and is made for gemstone cementing.
I would take the bracelet to a respected and trusted jewelry or watch repair shop. Ideally, the shop will have been in business for years so you can feel assured that they are not a fly-by-night company. You could also ask antique jewelry dealers where they take things that require repair or cleaning.
Almost any broken piece of jewelry can be fixed. Sometimes it's a simple clasp replacement, but sometimes it can be a little costly. If it's set in a metal(like silver), then you should be able to find a good silversmith(really evaluate him), who can weld it back together. There are never any guarantees, however.