This is a great question! In my opinion, chapters 1, 29, and 9 are the most significant.
Chapter 1 presents the setting: at first,the reader sees the rain leaving the landscape, the weeds and crops dying, and the wind howling. The Dust Bowl has begun. Steinbeck illustrates a very sad and somber mood in just the first three pages. Even though the dust covers everything from the earth to the people, Steinbeck illustrates the strengh of these people by using adjectives such as "hard and angry and resistant" (Steinbeck 6). Plus, the women and children watch the men to see if they would "break," but "no misfortune was too great to bear if their men were whole" (Steinbeck 7). This "wholeness" juxtaposes with Emerson's "Oversoul" theory, where all life on earth is connected as one bond--one completeness. This becomes evident in chapter 29 because Steinbeck goes back to the women and children watching the men to see if "the break" will come. In chapter 29, Steinbeck states that "the break would never come as long as fear could turn to wrath" (Steinbeck 592). In this chapter the reader is almost back to the beginning--full circle. Ironically, instead of a devastating drout, there is a flood. Regardless of the conditions and as long as these migrants stick together, then no one can take away their spirit to survive or their quest for a better life. They know the importance of "sticking" together and helping each other. It is called humanism. Chapter 30 then illustrates a true act of humanism and the theory of the "Oversoul" with Rose of Sharon's gift of life. Therefore, I think these two chapters are important because of the connection they have from the beginning of the novel to the end.
Chapter 9 is also significant because it is the "bitterness" chapter, which alludes to the title of the novel. The migrants have nothing left except what few belongings they can carry. They sell the farming supplies for absolutely nothing and are leaving behind the only life they have ever known. This refers to the Jefferson Agrarian theory that once a person is removed from his land, which is his life force, then that person will deteriorate just as the land will die once that person leaves because nature and man are connected--Oversoul. The word "bitterness" is mentioned five times, mainly as metaphors. The migrants are "bitter" because they have been forced from their land, their home. They have nothing but their memories to take with them, and no one cares. In this chapter, the "wrath" begins to show for the first time. From this chapter forward, the reader sees exactly why these people become so hardened and so angry at those who could care less whether the migrants live or die. Wealth and greed of the tenant farmers push the migrants to take action. Moreover, this chapter signifies the beginning of the wrath that will build and build until action replaces thought.