  Let $(\Sigma, \sigma)$ be a dynamical system, and let $U\subset \Sigma$.
Consider the survivor set \[ \Sigma_U=\{x\in \Sigma\mid \sigma^n(x)\notin
U\textrm{for all}n\} \] of points that never enter the subset $U$. We study the
size of this set in the case when $\Sigma$ is the symbolic space associated to
a self-affine set $\Lambda$, calculating the dimension of the projection of
$\Sigma_U$ as a subset of $\Lambda$ and finding an asymptotic formula for the
dimension in terms of the K\"aenm\"aki measure of the hole as the hole shrinks
to a point. Our results hold when the set $U$ is a cylinder set in two cases:
when the matrices defining $\Lambda$ are diagonal, and when they are such that
the pressure is differentiable at its zero point, and the K\"aenm\"aki measure
is a strong-Gibbs measure.
