  In the paper we prove that, for $\kappa\in(0,8)$, the $n$-point boundary
Green's function of exponent $\frac8\kappa -1$ for chordal SLE$_\kappa$ exists.
We also prove that the convergence is uniform over compact sets and the Green's
function is continuous. We also give up-to-constant bounds for the Green's
function.
