Abstract : We present the first maximum-entropy maps reconstructed from visibility amplitudes obtained with an optical long-baseline interferometer. They show the Be shell star zeta Tauri. In the continuum at 550 nm the star is an unresolved point source, whereas in the light of the H-alpha line an extended, elongated structure is observed. The best-fit parameters of an elliptical Gaussian model are: major axis a = 3.55 +/- 0.33 mas, axial ratio r = 0.30 +/- 0.03, position angle phi = -59 deg +/- 4 deg. The morphology of the H-alpha emission region is most easily interpreted as a disk seen almost edge-on; if this disk is axially symmetric, a limit for the inclination i greater than or equal to 73 deg can be derived. Our observations provide further evidence for the equatorial disk model of Be stars.