Let $X=(X_1,\dots ,X_m)$ be an infinitely degenerate system of vector fields, ${\mathrm{\Delta }}_X=\sum _{j=1}^m{X}_j^{\ast }{X}_j$, where $X_j^{\ast }$ is the formal adjoint of $X_j$. By employing the fixed point theorem, we obtain the existence of solutions to the degenerate parabolic equation $u_t={\mathrm{\Delta }}_{X}u+u\log |u|.$