  Recent observations of the low-mass X-ray binary 4U 1636-53 with the Rossi
X-ray Timing Explorer show, for the first time, a kiloHertz quasi-periodic
oscillation (kHz QPO) peak separation that exceeds the neutron star spin
frequency as inferred from burst oscillations. This strongly challenges the
sonic-point beat frequency model for the kHz QPOs found in low-mass X-ray
binaries. We detect two simultaneous kHz QPOs with a frequency separation of
323.3+-4.3 Hz in an average Fourier power spectrum of observations obtained in
September 2001 and January 2002. The lower kHz QPO frequency varied between 644
Hz and 769 Hz. In previous observations of this source the peak separation
frequency was ~250 Hz when the lower kHz QPO frequency was ~900 Hz. Burst
oscillations occur in 4U 1636-53 at ~581 Hz and possibly at half that frequency
(290.5 Hz). This is the first source where the peak separation frequency is
observed to change from less than (half) the burst oscillation frequency to
more than that. This observation contradicts all previously formulated
implementations of the sonic-point beat frequency model except those where the
disk in 4U 1636-53 switches from prograde to retrograde.
