Configuration space integrals have in recent years been used for studying the cohomology of spaces of (string) knots and links in $mathbb{R}^n$ for $n>3$ since they provide a map from a certain differential algebra of diagrams to the deRham complex o
f differential forms on the spaces of knots and links. We refine this construction so that it now applies to the space of homotopy string links -- the space of smooth maps of some number of copies of $mathbb{R}$ in $mathbb{R}^n$ with fixed behavior outside a compact set and such that the images of the copies of $R$ are disjoint -- even for $n=3$. We further study the case $n=3$ in degree zero and show that our integrals represent a universal finite type invariant of the space of classical homotopy string links. As a consequence, we obtain configuration space integral expressions for Milnor invariants of string links.
