PhD supervisor is taking really long to read my thesis
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.
While dan1111's answer is good, I have a different perspective.
First, calm down. Asking him 3 times a week about something is way too often. To calm down, see the points below.
Second, it sounds like you didn't agree on any timeline for the thesis writing process and feedback, but you're concerned about it so you should have this discussion.
Third, it's perhaps not a big deal if your advisor doesn't give you critical feedback during the initial writing process, and I don't know that this is so common. Possibly when you write later chapters that you will realize some ways you want to revise your earlier chapters anyway. Your advisor and committee will give feedback before or at your defense, and maybe your advisor should provide feedback once or twice before you arrange the defense just to make sure the thesis is reasonable (this should be discussed in your conversation about the timeline). I don't think I gave my advisor drafts of my thesis chapter by chapter, but just a full draft when I was done (though he had given me feedback on paper write-ups beforehand).
I concur with Kimball's first suggestion: calm down. My second observation is that it appears you feel entitled to have your supervisor help you: "I wish he just understood that he HAS to do it" and "I need to find a way to push him to do his job." These statements have a very egotistical tone to them. Your supervisor doesn't have to do anything. His taking you on as a student is adding more to his workload so you should be gracious he took you on in the first place. I think a lot of PhD students misunderstand this (I know I did). Editing your drafts is a small part of his job, just remember that.
My suggestion, go and meet with your supervisor and explain your concerns. If you want to be done by a certain date, let him know. I met with my advisor once and we had this exact conversation about when I was going to graduate and we set some tentative deadlines. My advisor was ridiculously slow at getting back to me with written feedback but he eventually did and all was fine. Now that I'm on the other side, I know why he was slow and I have no problem with it.
The bottom line, talk with him and do not go above his head. If you go above him without telling him first, depending on how spiteful (and tenured) he is, you may have to find yourself another supervisor. He may have a lot of work just pop up and might not have time to have you as a student anymore or the work you are doing is no longer good enough to earn a PhD. Probably won't happen but why take the chance of potentially angering your supervisor.