Do you agree with the Chief that the course of events leading to the violent episode between McMurphy and Nurse Ratched was inevitable? Why or why not?

I do believe that the violent conflict between Nurse Ratched and McMurphy is inevitable because of who they are as characters. They both are strong-willed and do not compromise their own characters. They stick to who they are, and given that their personalities are conflicting, the ending conflict between them is inevitable.
McMurphy is a joker and a gambler. He is not afraid of the Big Nurse. Chief Bromden observes the effect McMurphy has on the rest of the Ward.

There was times that week when I’d hear that full-throttled laugh, watch [McMurphy] scratching his belly and stretching and yawning and leaning back to wink at whoever he was joking with, everything coming to him just as natural as drawing breath, and I’d quit worrying about the Big Nurse and the Combine behind her. I’d think he was strong enough being his own self that he would never back down the way she was hoping he would. I’d think, maybe he truly is something extraordinary. He’s what he is, that’s it. Maybe that makes him strong enough, being what he is. The Combine hasn’t got to him in all these years; what makes the nurse think she’s gonna be able to do it in a few weeks? He’s not gonna let them twist him and manufacture him.

This quote shows how strong McMurphy's character is and how he won't back down, no matter what. It also shows how this threatens Nurse Ratched and how she will persist in trying to take him down.
Nurse Ratched longs for order and control. She enforces this and tells the patients it is for their own good.

Please understand: We do not impose certain rules and restrictions on you without a great deal of thought about their therapeutic value. A good many of you are in here because you could not adjust to the rules of society in the Outside World, because you refused to face up to them, because you tried to circumvent them and avoid them. At some time—perhaps in your childhood—you may have been allowed to get away with flouting the rules of society. When you broke a rule you knew it. You wanted to be dealt with, needed it, but the punishment did not come. That foolish lenience on the part of your parents may have been the germ that grew into your present illness. I tell you this hoping you will understand that it is entirely for your own good that we enforce discipline and order.

Chief Bromden often talks about a combine. He is observing that Nurse Ratched is part of a larger system of oppression.

McMurphy doesn’t know it, but he’s onto what I realized a long time back, that it’s not just the Big Nurse by herself, but it’s the whole Combine, the nation-wide Combine that’s the really big force, and the nurse is just a high-ranking official for them.

This quote shows how the two characters, McMurphy and Nurse Ratched, are opposing forces. The entire novel shows conflict between the two of them. This eventually leads to violence, as neither character is willing to back down or change who they are.
You might have a different opinion, or you might have a different reason for believing the conflict was inevitable. Be sure to use quotes to back up your argument.