Can I reuse parts of a chapter from a text book in my thesis? This question is related to this one. Only this time it's not about a journal paper but a chapter in a text book.

I am first author of the chapter in the text book that was published by a renowned publisher. I would like to reuse parts of the chapter for my PhD thesis (including a citation, of course). 

Is this acceptable? Is there anything different with respect to the situation with a "normal" paper? Is there anything I need to pay special attention to?

EDIT: The publisher allows reusing my own work in my thesis.
I did this in my thesis - my introduction was going cover a lot of information overlapping 3 textbook chapters I'd written, and I really didn't want to write it all again!

I did check with the publisher first, however (just an email asking for their consent), and added an acknowledgement to them in my acknowledgements page. I'm sure this was probably over-zealous, but it felt better to err on that side of things.