EXCITABLE media are physical, chemical or biological systems in which energy dissipation in disturbed regions is compensated by energy supply(1-4), so that the media can support waves without attenuation. Well-known examples are nervous tissue, heart muscle, retinae, aggregating amoebae and the autocatalytic Belousov-Zhabotinsky (BZ) reaction. Most familiar in such systems are periodic target and spiral waves, but a number of simulations(5-11) have suggested that disordered waves can also occur in a homogenous and motionless excitable medium. In all experimental observations reported so far, however, hydrodynamic flow(12,13) or inhomogeneities(14,15) were necessary to induce disorder. Here we present experimental evidence for disordered chemical waves in a convection-free and homogeneous medium, a gel containing a light-sensitive BZ reaction mixture. We find instabilities transverse to the wavefront (’ripples’), wave breakup leading to aperiodic spiral formation, labyrinthine structures, and erratic motion of non-spiralling wave fragments. The formal analogy of the BZ reagent with other excitable media suggests that this disordered behaviour may be generic.