  Charge order is commonly believed to compete with superconducting order. An
intertwined form of superconducting wave function, known as pair-density-wave
(PDW) order, has been proposed; however, there has been no direct evidence,
theoretical or experimental, that it forms the ground state of any cuprate
superconductor. As a test case, we consider \lbco\ with $x=1/8$, where charge
and spin stripe orders within the CuO$_2$ planes compete with three-dimensional
superconducting order. We report measurements of the superconducting critical
current perpendicular to the planes in the presence of an in-plane magnetic
field. The variation of the critical current with orientation of the field is
inconsistent with a theoretical prediction specific to the PDW model. It
appears, instead, that the orientation dependence of the critical-current
density might be determined by a minority phase of $d$-wave superconductivity
that is present as a consequence of doped-charge inhomogeneity.
