In this work we study the transport properties of point particles in a polygonal billiard chain. The dynamics in these billiards has different properties depending on the parameters of the system. In all cases the Liapunov exponents and the Kolmogorov-Sinai entropy are zero, in this sense there is no microscopic chaos. We find, from numerical simulations, that for certain parameters there is diffussion as well as heat transport. On the other hand for other set of parameters transport is anomalous.