  We report the identification of cyclical changes in the orbital period of the
eclipsing dwarf nova Z Cha. We used times of mid-eclipse collected from the
literature and our new eclipse timings to construct an
observed-minus-calculated diagram covering 30 years of observations
(1972-2002). The data present cyclical variations that can be fitted by a
linear plus sinusoidal function with period 28+/-2 yr and amplitude 1.0+/-0.2
minute. The statistical significance of this period by an F-test is larger than
99.9%. The derived fractional period change, Delta P/P= 4.4 x 10^{-7}, is
comparable to that of other short-period cataclysmic variables (CVs), but is
one order of magnitude smaller than those of the long-period CVs. Separate fits
to the first and second half of the data lead to ephemerides with quite
different cycle periods and amplitudes, indicating that the variation is not
sinusoidal or, most probably, is not strictly periodic. The observed cyclical
period change is possibly caused by a solar-type magnetic activity cycle in the
secondary star. An incremental variation in the Roche lobe of the secondary
star of Delta R_{L2}/R_{L2} = 1.7 x 10^{-4} is required in order to explain
both the observed period change and the modulation of the quiescent brightness
previously reported by Ak, Ozkan & Mattei.
