  We consider a transient chordal SLE$_\kappa(\rho_1,\dots,\rho_m)$ curve
$\eta$ in $\mathbb{H}$ from $w$ to $\infty$ with force points $ v_1> \cdots
>v_m$ in $(-\infty,w^-]$, which intersects and is not boundary-filling on
$(-\infty,v_m)$. The main result is that there is an atomless locally finite
Borel measure $\mu_\eta$ on $\eta\cap (-\infty,v_m]$ such that for any $v<v_m$,
the $d$-dimensional Minkowski content of $\eta\cap [v,v_m]$ exists and equals
$\mu_\eta [v,v_m]$, where $d=\frac{(\sum \rho_j+4)(\kappa-4-2\sum
\rho_j)}{2\kappa}$ is the Hausdorff dimension of $\eta\cap [v,v_m]$. In the
case that all $\rho_j=0$, this measure agrees with the covariant measure
derived in [Alberts-Sheffield, 2011] for chordal SLE$_\kappa$ up to a
multiplicative constant. %Such measure, called Minkowski content measure,
satisfies conformal covariance properties. We call such measure a Minkowski
content measure, extend it to a class of subsets of ${\mathbb{R}}^n$, and prove
that they satisfy conformal covariance. To construct the Minkowski content
measure on $\eta\cap [v,v_m]$, we follow the standard approach to derive the
existence and estimates of the one- and two-point boundary Green's functions of
$\eta$ on $(-\infty,v_m)$, which are the limits of the rescaled probability
that $\eta$ passes through small discs or open real intervals centered at
points on $(-\infty,v_m)$.
