  We study the properties of a quasi-one dimensional superconductor which
consists of an alternating array of two inequivalent chains. This model is a
simple charicature of a locally striped high temperature superconductor, and is
more generally a theoretically controllable system in which the superconducting
state emerges from a non-Fermi liquid normal state. Even in this limit,
``d-wave like'' order parameter symmetry is natural, but the superconducting
state can either have a complete gap in the quasi-particle spectrum, or gapless
``nodal'' quasiparticles. We also find circumstances in which antiferromagnetic
order (typically incommensurate) coexists with superconductivity.
