The wetting and dewetting of chemically structured substrates with striped surface domains is studied theoretically. The lyophilic stripes and the lyophobic substrate are characterized by different contact angles θγ and θδ, respectively. We determine the complete bifurcation diagram for the wetting morphologies (i) on a single lyophilic stripe and (ii) on two neighboring stripes separated by a lyophobic one. We find that long channels can only be formed on the lyophilic stripes if the contact angle θγ is smaller than a certain threshold value θch(V) which depends only weakly on the volume V and attains the finite value θch(∞) in the limit of large V. This asymptotic value is equal to θch(∞)=arccos(π/4)≃38° for all lyophobic substrates with θδ⩾π/2. For a given value of θγ<θch(∞), the extended channels spread onto the lyophilic stripes with essentially constant cross section.