In this paper, the following third-order nonlinear delay differential equation with periodic coefficients $$x'''(t) + p(t)x''(t)+q(t)x'(t)+r(t)x(t)= f\bigl(t,x(t),x(t-au(t))\bigr) + \frac{d}{dt}g\bigl(t,x(t-au(t))\bigr),$$ 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 nonlinear delay differential equation.