Using deep rest-frame optical spectroscopy from the Large Early Galaxy Astrophysical Census (LEGA-C) survey, conducted using VIMOS on the ESO Very Large Telescope, we search for low-ionization [O ii] lambda lambda 3726,3729 emission in the spectra of a mass-complete sample of z approximate to 0.85 galaxies. We find that 59% of UVJ-quiescent (i.e., non-star-forming) galaxies in the sample have [O ii] emission detected above our completeness limit of 1.5 angstrom, and the median-stacked spectrum of the remaining sample also shows [O ii] emission. The overall fraction of sources with [O ii] above our equivalent width limit is comparable to what we find in the low-redshift universe from GAMA and MASSIVE, except perhaps at the highest stellar masses (>10(11.5) M (circle dot)). However, stacked spectra for the individual low-equivalent-width systems uniquely indicates ubiquitous [O ii] emission in the higher-z LEGA-C sample, with typical [O ii] luminosities per unit stellar mass that are a factor of x3 larger than the lower-z GAMA sample. Star formation at higher-z could play a role in producing the [O ii] emission, although it is unlikely to provide the bulk of the ionizing photons. More work is required to fully quantify the contributions of evolved stellar populations or active galactic nuclei to the observed spectra.