Superconductivity (SC) and ferromagnetism (FM) are in general antagonistic, which makes their coexistence very rare. Following our recent discovery of robust coexistence of SC and FM in RbEuFe$_4$As$_4$ [Y. Liu et al., arXiv: 1605.04396 (2016)], here we report another example of such a coexistence in its sister compound CsEuFe$_4$As$_4$, synthesized for the first time. The new material exhibits bulk SC at 35.2 K and Eu$^{2+}$-spin ferromagnetic ordering at 15.5 K, demonstrating that it is a new robust ferromagnetic superconductor.