We have observed the ultra-compact low-mass X-ray binary (LMXB) 1A 1246-588 with the Rossi X-ray Timing Explorer (RXTE). In this manuscript we report the discovery of a kilohertz quasi-periodic oscillation (QPO) in 1A 1246-588. The kilohertz QPO was only detected when the source was in a soft high-flux state reminiscent of the lower banana branch in atoll sources. Only one kilohertz QPO peak is detected at a relatively high frequency of 1258+-2 Hz and at a single trial significance of more than 7 sigma. Kilohertz QPOs with a higher frequency have only been found on two occasions in 4U 0614+09. Furthermore, the frequency is higher than that found for the lower kilohertz QPO in any source, strongly suggesting that the QPO is the upper of the kilohertz QPO pair often found in LMXBs. The full-width at half maximum is 25+-4 Hz, making the coherence the highest found for an upper kilohertz QPO. From a distance estimate of ~6 kpc from a radius expansion burst we derive that 1A 1246-588 is at a persistent flux of ~0.2-0.3 per cent of the Eddington flux, hence 1A 1246-588 is one of the weakest LMXBs for which a kilohertz QPO has been detected. The root-mean-square (rms) amplitude in the 5-60 keV band is 27+-3 per cent, this is the highest for any kilohertz QPO source so far, in line with the general anti-correlation between source luminosity and rms amplitude of the kilohertz QPO peak identified before. Using the X-ray spectral information we produce a colour-colour diagram. The source behaviour in this diagram provides further evidence for the atoll nature of the source.
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