We present the first results from a study of OVI absorption around galaxies at z<1.44 using data from a near-infrared grism spectroscopic Hubble Space Telescope Large Programme, the Quasar Sightline and Galaxy Evolution (QSAGE) survey. QSAGE is the first grism galaxy survey to focus on the circumgalactic medium at z~1, providing a blind survey of the galaxy population. The galaxy sample is H{alpha} flux limited (f(H{alpha})>2x10^-17^erg/s/cm^2^) at 0.68<z<1.44, corresponding to >~0.2-0.8M_{sun}_/yr. In this first of 12 fields, we combine the galaxy data with high-resolution STIS and COS spectroscopy of the background quasar to study OVI in the circumgalactic medium. At z~1, we find OVI absorption systems up to b~350kpc (~4R_vir_) from the nearest detected galaxy. Further, we find ~50 per cent of >~1M_{sun}_/yr star-forming galaxies within 2R_vir_ show no associated OVI absorption to a limit of at least N(OVI)=10^13.9^cm^-2^. That we detect OVI at such large distances from galaxies and that a significant fraction of star-forming galaxies show no detectable OVI absorption disfavours outflows from ongoing star formation as the primary medium traced by these absorbers. Instead, by combining our own low- and high-redshift data with existing samples, we find tentative evidence for many strong (N(OVI)>10^14^cm^-2^) OVI absorption systems to be associated with M_*_~10^9.5-10^M_{sun}_ mass galaxies (M_halo_~10^11.5-12^M_{sun}_ dark matter haloes), and infer that they may be tracing predominantly collisionally ionized gas within the haloes of such galaxies.