In this paper, the following third-order nonlinear delay differential equation with periodic coefficients

x′′′(t)+p(t)x′′(t)+q(t)x′(t)+r(t)x(t)=f(t,x(t),x(t-τ(t)))+c(t)x′(t-τ(t)),

is considered. By employing Green's function and Krasnoselskii's fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.