We present coordinated Chandra X-ray Observatory and Karl G. Jansky Very Large Array observations of the transitional millisecond pulsar PSR J1023+0038 in its low-luminosity accreting state. The unprecedented five hours of strictly simultaneous X-ray and radio continuum coverage for the first time unambiguously show a highly reproducible, anti-correlated variability pattern. The characteristic switches from the X-ray high mode into a low mode are always accompanied by a radio brightening with duration that closely matches the X-ray low mode interval. This behavior cannot be explained by a canonical inflow/outflow accretion model where the radiated emission and the jet luminosity are powered by, and positively correlated with, the available accretion energy. We interpret this phenomenology as alternating episodes of low-level accretion onto the neutron star during the X-ray high mode that are interrupted by rapid ejections of plasma by the active rotation-powered pulsar, possibly initiated by a reconfiguration of the pulsar magnetosphere, that cause a transition to a less luminous X-ray mode. The observed anti-correlation between radio and X-ray luminosity has an additional consequence: transitional MSPs can make excursions into a region of the radio/X-ray luminosity plane previously thought to be occupied solely by black hole X-ray binary sources. This complicates the use of this luminosity relation to identify candidate black holes, suggesting the need for additional discriminants when attempting to establish the true nature of the accretor.
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