  We prove Helly-type theorems for line transversals to disjoint unit balls in
$\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit
balls in $\R^d$ has a line transversal if, for some ordering $\prec$ of the
balls, any subfamily of 2d balls admits a line transversal consistent with
$\prec$. We also prove that a family of $n \geq 4d-1$ disjoint unit balls in
$\R^d$ admits a line transversal if any subfamily of size $4d-1$ admits a
transversal.
