PhD supervisor is taking really long to read my thesis I am at the final point of my pretty satisfying PhD. I like working alone and I did not need constant supervision, and I had a pretty good relationship with my supervisor until now. I noticed in the past that when it was time to proof-read papers, it took EXTREMELY LONG TIME to do it, and almost always waited until the day of the deadline (however, it was always corrected at the end). 

Now that it is time for my thesis, though, things are getting difficult. I sent  the first experimental chapter more than one month ago, and it still hasn't been read, every time saying that there has some other deadline. I have been asking three times a week, and every time the the same thing is said. Of course, I don't find any pleasure in keep pressuring my supervisor, and I wish it was understood that it HAS to be done. I am afraid that it he takes 1+ month to check a chapter, it will take a year to read the whole stuff!
In the meantime I have kept working on the thesis and I will finish writing the first draft soon, but it hasn't been corrected yet. I am not sure about the course of action here. How to deal with this situation?

Should I talk with the director of studies? Should I keep pressuring my supervisor? Should I give a deadline? 
If I decide to talk with the director of studies, should I tell my supervisor first? 

The main point is that until now I have had a good relationship and I don't want to ruin it just now. However, I need to find a way to push to get the supervisor to complete the job. 



Edit to add some related details from the comments:


I'm in the UK, and my research is in a field related to psychology.
My second supervisor is not involved in my project, and it wouldn't be appropriate for me to contact them for this question.
My scholarship ended a few months back, and I'm now being paid as a research assistant with my supervisor for a few more months.
All research work has been completed, the analysis are done, and I'm almost finished with writing. Changing departments is not an option.


EDIT: Thank you to everybody for your help. This is the way I proceeded: without mentioning to my supervisor about this chapter again, I just discussed about the timing to complete my PhD, mentioning that I plan to finish writing in around one month. This requires me to complete some bureaucratic paperwork soon, which means that we have to set up some deadlines, find examiners etc., which also means that my thesis will be corrected before a deadline. Since my supervisor works better with deadlines, I think that this method will work. Therefore, I ignored the particular problem about correcting the single chapter, and I used the main topic (finishing my PhD) as a way to get things rolling. Not sure if this is the best solution, but I think it may work for me.
Thank you again, your support has been very appreciated.
A good starting assumption is that your supervisor has good intentions, but like many of us, has trouble getting things done because of workload and/or procrastination.

Artificial deadlines may help.  Perhaps your supervisor is too busy right now but would be able to agree on a date several weeks in the future by which he can read the chapter.  Or even better, perhaps you could agree an overall schedule for completing your thesis, including deadlines by which you will send each chapter, he will review it, and so on.  This could help prevent the problem from recurring in the future.

If this doesn't work, I would have a chat and share your concerns with him about how you feel this is needed for your own successful completion of your thesis.  

If all of this still doesn't have any impact, you are in a tough position.  You are dependent on your supervisor, but outside of extreme situations, there is no real formal mechanism requiring his action.  You could try getting your second supervisor involved.  Even if you have had no contact so far, you do have a formal relationship with this person, and that is a good enough basis to do so.  

Talking to the director of studies would be a last resort.  It probably isn't worthwhile until the continued inaction is clearly going to delay your PhD completion.  If you want to maintain a good relationship, I would discuss this with your supervisor first, making it clear that the delays are about to have a big impact on your life, and you feel you have no other choice.