We consider a one-dimensional lattice of expanding antisymmetric maps with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as the parameter grows beyond some critical value. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as the coupling approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system.