[en] We present the results of precision gamma-ray timing measurements of the binary millisecond pulsar PSR J2339–0533, an irradiating system of the “redback” type, using data from the Fermi Large Area Telescope. We describe an optimized analysis method to determine a long-term phase-coherent timing solution spanning more than six years, including a measured eccentricity of the binary orbit and constraints on the proper motion of the system. A major result of this timing analysis is the discovery of an extreme variation of the nominal 4.6 hr orbital period $P_{\mathrm{o}\mathrm{r}\mathrm{b}}$ over time, showing alternating epochs of decrease and increase. We inferred a cyclic modulation of $P_{\mathrm{o}\mathrm{r}\mathrm{b}}$ with an approximate cycle duration of 4.2 yr and a modulation amplitude of $\mathrm{\Delta <!--\; ??\; -->}{P}_{\mathrm{o}\mathrm{r}\mathrm{b}}/P_{\mathrm{o}\mathrm{r}\mathrm{b}}=2.3\times <!--\; ??\; -->{10}^{-<!--\; ???\; -->7}$. Considering different possible physical causes, the observed orbital-period modulation most likely results from a variable gravitational quadrupole moment of the companion star due to cyclic magnetic activity in its convective zone.