Which of the following works is not written by Chinua Achebe?

The correct option is "Weep not, Child".

To understand why this is the correct answer, let's look at the authorship of each of the works listed in the options:
1. Arrow of God: This is a prominent novel published in 1964 by the Nigerian author Chinua Achebe. It is the third book in his African Trilogy, following Things Fall Apart and No Longer at Ease.
2. No Longer at Ease: This novel, published in 1960, was also written by Chinua Achebe. It serves as the second work in his famous African Trilogy.
3. An Image of Africa: Officially titled "An Image of Africa: Racism in Conrad's 'Heart of Darkness'", this is a highly influential post-colonial lecture and essay published by Chinua Achebe in 1977.
4. Weep not, Child: This celebrated historical novel, published in 1964, was written by the Kenyan author Ngũgĩ wa Thiong'o (initially published under the name James Ngugi), not by Chinua Achebe.

Therefore, among the given choices, "Weep not, Child" is the only work that was not written by Chinua Achebe.