As mrmikel said you don't have to split up your file - but it might not work well on all readers and its common practice to break up the book into multiple files.
You don't want to insert a chapter break for each chapter. What you want to do is to insert a chapter marker just before every chapter by using Edit->Insert Chapter Marker or ctrl-shift-return. Just put your cursor at the beginning of the chapter name in book view and insert the marker. Once you've inserted the marker everywhere you want it, then use Edit->Split at chapter markers (F6 key). And your book will be split in one go. Make sure you save a backup copy first