  In this paper, we classify the Einstein hypersurfaces of $\mathbb{S}^n \times
\mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$. We use the characterization
of the hypersurfaces of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n
\times \mathbb{R}$ whose tangent component of the unit vector field spanning
the factor $\mathbb{R}$ is a principal direction and the theory of
isoparametric hypersurfaces of space forms to show that Einstein hypersurfaces
of $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ must
have constant sectional curvature.
