  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.
