We present the serendipitous radio-continuum discovery of a likely Galactic supernova remnant (SNR) G305.4–2.2. This object displays a remarkable circular symmetry in shape, making it one of the most circular Galactic SNRs known. Nicknamed Teleios due to its symmetry, it was detected in the new Australian Square Kilometre Array Pathfinder (ASKAP) Evolutionary Map of the Universe (EMU) radio–continuum images with an angular size of 1 320×1 260 and PA = 0◦. While there is a hint of possible Hα and gamma-ray emission, Teleios is exclusively seen at radio–continuum frequencies. Interestingly, Teleios is not only almost perfectly symmetric, but it also has one of the lowest surface brightnesses discovered among Galactic SNRs and a steep spectral index of α=–0.6±0.3. Our best estimates from HI studies and the –D relation place Teleios as a type Ia SNR at a distance of either ∼2.2 kpc (near-side) or ∼7.7 kpc (far-side). This indicates two possible scenarios, either a young (under 1 000 yr) or a somewhat older SNR (over 10 000 yr). With a corresponding diameter of 14/48 pc, our evolutionary studies place Teleios at the either early or late Sedov phase, depending on the distance/diameter estimate. However, our modelling also predicts X-ray emission, which we do not see in the present generation of eROSITA images. We also explored a type Iax explosion scenario that would point to a much closer distance of <1 kpc and Teleios size of only ∼3.3 pc, which would be similar to the only known type Iax remnant SN1181. Unfortunately, all examined scenarios have their challenges, and no definitive Supernova (SN) origin type can be established at this stage. Remarkably, Teleios has retained its symmetrical shape as it aged even to such a diameter, suggesting expansion into a rarefied and isotropic ambient medium. The low radio surface brightness and the lack of pronounced polarisation can be explained by a high level of ambient rotation measure (RM), with the largest RM being observed at Teleios’s centre.