Chomp was introduced by Gale in 1974 \cite{Gale1974}. In the same paper, Gale reported that the $3\times n$ games had been completely analyzed for $n\le 100$, with a unique winning first move in every case, and asked whether winning first moves are unique in general. Although the general uniqueness statement is false \cite[Section~7.1]{BrouwerEtAl2005}, we prove that the three-row uniqueness phenomenon suggested by Gale's computations holds for all $n$: every $3\times n$ Chomp rectangle has exactly one winning opening move. This settles the three-row case of Gale's 52-year-old first-move uniqueness question. The proof is carried out in the two-variable recurrence introduced by Brouwer, Horváth, Molnár-Sáska, and Szabó \cite{BrouwerEtAl2005} for the function $f(q,r)$ whose values encode the $P$-positions. The main local ingredient is a rightmost-hole principle: if a value $p$ is absent from the set $C(q,r)$ but belongs to all corresponding sets $C(t,r)$ for $q