  We discover a robust coexistence of superconductivity and ferromagnetism in
an iron arsenide RbEuFe$_4$As$_4$. The new material crystallizes in an
intergrowth structure of RbFe$_2$As$_2$ and EuFe$_2$As$_2$, such that the Eu
sublattice turns out to be primitive instead of being body-centered in
EuFe$_2$As$_2$. The FeAs layers, featured by asymmetric As coordinations, are
hole doped due to charge homogenization. Our combined measurements of
electrical transport, magnetization and heat capacity unambiguously and
consistently indicate bulk superconductivity at 36.5 K in the FeAs layers and
ferromagnetism at 15 K in the Eu sublattice. Interestingly, the Eu-spin
ferromagnetic ordering belongs to a rare third-order transition, according to
the Ehrenfest classification of phase transition. We also identify an
additional anomaly at $\sim$ 5 K, which is possibly associated with the
interplay between superconductivity and ferromagnetism.
