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If ϕ is an analytic self-mapping of the unit disc D and if $H^2\left(D\right)$ is the Hardy-Hilbert space on D, the composition operator $C_{\varphi }$ on $H^2\left(D\right)$ is defined by $C_{\varphi }\left(f\right)=f\circ \varphi$. In this article, we consider which Toeplitz operators $T_f$ satisfy $T_f{C}_{\varphi }=C_{\varphi }{T}_f$