Final answer:
The β chain of the TCR gene variable region possesses a D segment.
Step-by-step explanation:
The T cell receptor (TCR) genes consist of variable (V), diversity (D), and joining (J) segments. The genes associated with the α chain of the TCR have Vα and Jα segments, while the genes associated with the β chain have Vβ, Dβ, and Jβ segments. Among these TCR gene variable regions, only the β chain possesses a "D" segment. Therefore, the correct answer is A. β.