We study the properties of a quasi-one-dimensional superconductor which con
sists of an alternating array of two inequivalent chains. This model is a s
imple caricature of a 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 lit-nit, "
d-wave-like" order parameter symmetry is natural, but the superconducting s
tate can either have a complete gap in the quasiparticle spectrum, or gaple
ss "nodal" quasiparticles. We also find circumstances in which antiferromag
netic order (typically incommensurate) coexists with superconductivity.