A critique is not the same as a book review, summary or book report, though it may have some elements from each. You need to read the book in a particular way to be able to write a critique. When you are familiar with it, reread the chapter asking yourself specific questions. You need to know the author's purpose for writing it and where it fits into his thesis.
A critique is not the same as a criticism, though you may criticize some aspects of the chapter. You need to read the chapter, thinking all the time of the author's purpose, asking what she has set out to do. Is her principle aim to persuade, entertain or inform? Ask yourself, whether in your opinion she has achieved her aim.
A person who has a background knowledge of the subject, the author and other similar or conflicting books and theories will be better placed to carry out a critique. This is because the reader will be able to see the chapter and book in the larger context. The informed reader will be able to decide whether this chapter breaks new ground or adds significantly to the debate.
If you have not written a critique before, you may be tempted to be over complimentary -- to only see the cleverness of the argument and the superior knowledge of the author. However, if the critique is part of an academic course, some criticism, provided it is backed by evidence, is perfectly acceptable. The reader would look for any examples of contradiction or a mere rehash of others' arguments. A critique would also consider the style of writing and the readability of the chapter.