We consider a layered superconductor with a complex order parameter wh
ose phase switches sign from one layer to the next. This system is sho
wn to exhibit gapless superconductivity for sufficiently large interla
yer pairing or interlayer hopping. In addition, this description is co
nsistent with experiments finding signals of time-reversal symmetry br
eaking in high-temperature superconductors only at the surface and not
in the sample bulk.