Lifting Divisors on a Generic Chain of Loops Let $C$ be a curve over a complete valued field with infinite residue field whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on $C$, confirming a conjecture of Cools, Draisma, Robeva, and the third author. Keywords:tropical geometry, Brill-Noether theory, special divisors on algebraic curvesCategories:14T05, 14H51