We present results from the first successful millimetre (combined 33 GHz and 35 GHz) observations of the neutron star X-ray binary Circinus X-1, using the Australia Telescope Compact Array. The source was clearly detected in all three observing epochs. We see strong evidence for a periastron flare beginning at MJD 55519.9 pm 0.04 with estimated peak flux densities of up to 50 mJy and which proceeds to decline over the following four days. We directly resolve jet structures on sub-arcsecond scales. Flux density variability and distance from the core of nearby components suggests recent shock re-energisation, though we are unable to directly connect this with the observed flare. We suggest that, if the emission is powered by an unseen outflow, then a phase delay exists between flare onset and subsequent brightening of nearby components, with flows reaching mildly relativistic velocities. Given resolved structure positions, in comparison to past observations of Cir X-1, we find evidence that jet direction may vary with distance from the core, or the sources precession parameters have changed.