We analyze the possibility of heavy-light tetraquark bound states by means of a chiral constituent quark model. The study is done in a variational approach. Special attention is paid to the contribution given by the different terms of the interacting potential and also to the role played by the different color channels. We find a stable state for both $qq\bar{c}\bar{c}$ and $qq\bar{b}\bar{b}$ configurations. Possible decay modes of these structures are analyzed.