  We report Karl G. Jansky Very Large Array (VLA) and Atacama Large Millimeter
Array (ALMA) spectroscopy in the redshifted molecular oxygen (O$_2$) 56.265~GHz
and 424.763~GHz transitions from the $z=0.88582$ gravitational lens towards
PKS\,1830$-$21. The ALMA non-detection of O$_2$ 424.763~GHz absorption yields
the $3\sigma$ upper limit $N({\rm O}_2) \leq 5.8 \times 10^{17}$~cm$^{-2}$ on
the O$_2$ column density, assuming that the O$_2$ level populations are
thermalized at the gas kinetic temperature of 80~K. The VLA spectrum shows
absorption by the CH$_3$CHO 56.185~GHz and 56.265~GHz lines, with the latter
strongly blended with the O$_2$ 56.265~GHz line. Since the two CH$_3$CHO lines
have the same equilibrium strength, we used the known CH$_3$CHO 56.185~GHz line
profile to subtract out the CH$_3$CHO 56.265~GHz feature from the VLA spectrum,
and then carried out a search for O$_2$ 56.265~GHz absorption in the residual
spectrum. The non-detection of redshifted O$_2$ 56.265~GHz absorption in the
CH$_3$CHO-subtracted VLA spectrum yields $N({\rm O}_2) \leq 2.3 \times
10^{17}$~cm$^{-2}$. Our $3\sigma$ limits on the O$_2$ abundance relative to
H$_2$ are then $X({\rm O}_2) \leq 9.1 \times 10^{-6}$ (VLA) and $X({\rm O}_2)
\leq 2.3 \times 10^{-5}$ (ALMA). These are $5-15$ times lower than the best
previous constraint on the O$_2$ abundance in an external galaxy. The low O$_2$
abundance in the $z= 0.88582$ absorber may arise due to its high neutral carbon
abundance and the fact that its molecular clouds appear to be diffuse or
translucent clouds with low number density and high kinetic temperature.
