  We define reflective modular forms on complex balls and use a method of
Gritsenko and Hulek to show that some ball quotients of dimensions 3, 4 and 5
are uniruled. We give examples of Hermitian lattices over the rings of integers
of imaginary quadratic fields $\mathbb{Q}(\sqrt{-1})$ and
$\mathbb{Q}(\sqrt{-2})$ for which the associated ball quotients are uniruled.
Our examples include the moduli space of 8 points on $\mathbb{P}^1$. Moreover,
we find that some of their Satake-Baily-Borel compactifications are rationally
chain connected modulo certain cusps.
