Why does Genesis 36 give a whole chapter to Esau's genealogy?

Because the genealogy's placement is its argument: Esau becomes a finished nation with chiefs, kings, and a land held as a possession — while Jacob still has nothing but a promise. The chapter closes one story so the other can continue.

The short answer is that the chapter is making an argument — and the argument is made by where it sits, not by anything it says outright.

Genesis 36 comes after Jacob has buried his father Isaac and before Joseph's story begins. Into that gap the narrator drops the complete national record of the brother who was not chosen. By the time you finish reading it, Esau has chiefs, kings, and a land held as a settled possession. Jacob, immediately afterward in Genesis 37:1, is still living as a sojourner on borrowed ground. The genealogy's position is the point: the non-elect line is finished and settled; the elect line has only a promise and is still waiting for it.

The word that organizes Genesis

The chapter announces itself with the Hebrew word תֹּלְדוֹת (toledot, H8435), which means "generations — the line of descent, family, and history." It is the structural backbone of the entire book of Genesis, the heading that organizes it into sections. And here, uniquely in the whole Bible, the same person gets two toledot headings: "these are the generations of Esau — he is Edom" (Genesis 36:1), and then again at verse 9, "these are the generations of Esau the father of Edom in the hill country of Seir." No other chapter gives one person this heading twice.

The doubling is deliberate. The first heading names the man; the second names the nation and its territory. The story of Esau and the story of Edom are each declared complete.

This is actually the second time Genesis has run this pattern. Ishmael, Abraham's non-elect son, got his own toledot and a complete genealogy in Genesis 25. But Ishmael's record is seven verses. Esau's is forty-three. Edom is the larger, more developed nation, and the chapter takes its time saying so — because the contrast with Jacob needs to land.

Running like a refrain

Four times in the chapter, the narrator fuses the man to the people: "Esau — he is Edom." The personal pronoun הוּא (hu') and the name עֵשָׂו (Esav) appear together at Genesis 36:1, 36:8, 36:19, and 36:43. The closing form is the fullest: "he is Esau the father of Edom." The chapter opens with "Esau — he is Edom" and ends with "Esau the father of Edom." Between those two clauses the man has become a people. That is the work the genealogy is doing.

When the next chapter begins, Genesis 37:2 opens with the eleventh and final toledot of Genesis — "these are the generations of Jacob." One brother is cataloged and complete. The other continues. The genealogy of the non-elect brother is the frame around the still-unfinished story of the elect one.

"And Jacob dwelt in the land of his father's sojournings." — Genesis 37:1

The whole chapter, forty-three verses of chiefs and kings and territory, is there to make that one sentence land harder. For the full study of what Genesis 36 is doing — the double toledot, the Lot-and-Abram echo, the king list, and the possession-versus-sojourning contrast — see The Line of Esau.