  We present the results of near-infrared (2 and 3 microns) monitoring of Sgr
A*-IR with 1 min time sampling using the natural and laser guide star adaptive
optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed
continuously for up to three hours on each of seven nights, between 2005 July
and 2007 August. Sgr A*-IR is detected at all times and is continuously
variable, with a median observed 2 micron flux density of 0.192 mJy,
corresponding to 16.3 magnitude at K'. These observations allow us to
investigate Nyquist sampled periods ranging from about 2 minutes to an hour.
Using Monte Carlo simulations, we find that the variability of Sgr A* in this
data set is consistent with models based on correlated noise with power spectra
having frequency dependent power law slopes between 2.0 to 3.0, consistent with
those reported for AGN light curves. Of particular interest are periods of ~20
min, corresponding to a quasi-periodic signal claimed based upon previous
near-infrared observations and interpreted as the orbit of a 'hot spot' at or
near the last stable orbit of a spinning black hole. We find no significant
periodicity at any time scale probed in these new observations for periodic
signals. This study is sensitive to periodic signals with amplitudes greater
than 20% of the maximum amplitude of the underlying red noise component for
light curves with duration greater than ~2 hours at a 98% confidence limit.
