We consider a periodic solution for a class of distributed delay differential equations. A period two solution for distributed delay differential equations, where the period is twice the maximum delay, is shown to satisfy a Hamiltonian system of ordinary differential equations, from which we can construct the period two solution for the distributed delay differential equation. The idea is based on Kaplan & Yorke (1974, JMAA) for a discrete delay differential equation. We present distributed delay differential equations that have periodic solutions expressed in terms of the Jacobi elliptic functions. Recent results are also discussed.