I read the third and . . . . . . . . fourth chapter of the book.

The use of definite article 'the' before the noun 'book', makes it clear that we are referring to a specific book and its chapters. Therefore it is imperative that we use 'the' before 'fourth chapter' to show that we are not referring to just any chapter of any book but a specific chapter of a specific book. Also when two or more nouns or adjectives refer to different persons or things, the article is used before each noun or adjective. Thus option C is the correct answer.