  We study the viscosity solutions to the first eigenvalue equation. We
consider $\Omega$ a bounded B-regular domain in $\mathbb{C}^n$ and we prove
that the Dirichlet problem $\Lambda_{1}(D_{\mathbb{C}}^2 u)=f$ in $\Omega$ and
$u=\varphi$ on $\partial\Omega$ admits a unique viscosity solution. We also
deal with viscosity theory for operators which are comparable to the first
eigenvalue operator.
