I started with Lit Review (16 months write up time), then methodology (8 months write up time), then analysis, discussion, findings (about three months write up time), then introduction and conclusions (about a month).
The order is dependent on the subject and many other factors,but it makes sense to start with a literature foundation. You can then work with this foundation and it will help you to make more sense of your data. it will also guide you in the right direction whilst you collect data.
Continuous reading and knowledge of papers in the area will be important throughout the entire duration of your doctoral studies. So why not writing this chapter whilst you go along and have to read anyway?