Depends on the model. Cheapos are riveted, better ones are held by Allen bolts.
Originally Posted by Rumblejohn
Here's some boilerplate that may be relevant:
Back in the old days, every tooth on a chainring was the same as every other tooth on that ring.
Beginning in the 1980s, however, Shimano started experimenting with different shaped teeth in different parts of the chainrings, with the aim of improving shifting.
Newer chainrings typically have some teeth much shorter than others, usually the teeth that are picking up the chain when the cranks are vertical (this is when chain tension is lowest, and is the best time to make the shift.
These special stubby teeth, often coupled with "shift assist" pins and ramps on the side of the chainrings, make a great improvement in shifting.
However, one drawback of this is that folks who aren't aware of this design will sometimes discover the short teeth and will assume that their chainrings are damaged or worn out! They aren't!
It is very rare to actually wear chainrings out, takes many, many thousands of miles with a worn-out chain. When a chainring is worn out, _all_ of the teeth show the wear, usually acquiring a hooked appearance on the sides of the teeth that drive the chain.
For further information on this, see: http://sheldonbrown.com/chains
Don't be embarrassed about this...this is a _very_ common question, so common that I have prepared this generic boilerplate response to save re-typing.
All the best,