Take a look at the sentence again:
Jean always nibbles around the pit of a cherry, just as if she were eating
a peach, because she is vain about her smile, she doesn't
want to chip a tooth on the hard center.
The blank space between want and to is completely correct. She doesn't want is a main clause. To chip a tooth on the hard center is an infinitive phrase. An infinitive phrase will begin with an infinitive like to chip. When you connect an infinitive phrase to the end of a main clause, you need no punctuation.
Go back to the sentence to try again.