  We prove a unique ergodicity theorem for singular holomorphic foliations of
$\mathbb{P}^3(\mathbb{C})$ with hyperbolic singularities and with an invariant
plane with no foliation cycle, in analogy with a result of Dinh-Sibony
concerning unique ergodicity for foliations of $\mathbb{P}^2(\mathbb{C})$ with
an invariant line. The proof is dynamical in nature and adapts the work of
Deroin-Kleptsyn to a singular context, using the fundamental integrability
estimate of Nguy\^en.
