  We show that the Heisenberg group $\mathbb{H}^n$ contains a measure zero set
$N$ such that every Lipschitz function $f\colon \mathbb{H}^n \to \mathbb{R}$ is
Pansu differentiable at a point of $N$. The proof adapts the construction of
small 'universal differentiability sets' in the Euclidean setting: we find a
point of $N$ and a horizontal direction where the directional derivative in
horizontal directions is almost locally maximal, then deduce Pansu
differentiability at such a point.
