  In this paper we obtain formulas for the distribution of the left-most
up-spin in the Heisenberg-Ising spin-1/2 chain with anisotropy parameter
$\Delta$, also known as the XXZ spin-1/2 chain, on the one-dimensional lattice
$\mathbb{Z}$ with domain wall initial conditions. We use the Bethe Ansatz to
solve the Schr$\"o$dinger equation and a recent antisymmetrization identity of
Cantini, Colomo, and Pronko (arXiv:1906.07636) to simplify the marginal
distribution of the left-most up-spin. In the $\Delta=0$ case, the distribution
$F_2$ arises. In the $\Delta \neq 0$ case, we propose a conjectural series
expansion type formula based on a saddle point analysis. The conjectural
formula turns out to be a Fredholm series expansion in the $\Delta \rightarrow
0$ limit and recovers the result for $\Delta = 0$.
