  We report the discovery ($20\sigma$) of kilohertz quasi-periodic oscillations
(kHz QPOs) at ~ 690 Hz from the transient neutron star low-mass X-ray binary
EXO 1745-248. We find that this is a lower kHz QPO, and systematically study
the time variation of its properties using smaller data segments with and
without the shift-and-add technique. The quality (Q) factor occasionally
significantly varies within short ranges of frequency and time. A high Q-factor
(264.5 +- 38.5) of the QPO is found for a 200 s time segment, which might be
the largest value reported in the literature. We argue that an effective way to
rule out kHz QPO models is to observationally find such high Q-factors, even
for a short duration, as many models cannot explain a high coherence. However,
as we demonstrate, the shift-and-add technique cannot find a very high Q-factor
which appears for a short period of time. This shows that the coherences of kHz
QPOs can be higher than the already high values reported using this technique,
implying further constraints on models. We also discuss the energy dependence
of fractional rms amplitude and Q-factor of the kHz QPO.
