First Draft
You should write about the project as you go along, restating your position as your understanding changes. Even a paragraph or a page once a week in your research log will help.
Plan to write your first draft early enough to submit it, chapter by chapter, to your adviser and to revise it on the basis of his or her comments. Set a deadline to complete a second draft well before the final due date so that your adviser has time to read it and you have time to make necessary further revisions.
Talking with your adviser after you complete each chapter may help decide what you need to do in order to complete the project. You may choose to continue investigating the sources outlined in your initial plan or to read something else instead. You may decide that you have read enough and should now revise your paper to more clearly expand your ideas.
Keep in mind that revising the final product of a research project will probably involve more than merely refining stylistic elements. You may have to do more research, write new sections, or even rethink the whole thing. In the end, the quality of your essay may depend on how much time you have set aside to rework your thoughts for the final draft.