We present initial results from an exploratory X-ray monitoring project of two groups of comparably luminous radio-quiet quasars ( RQQs ) . The first consists of four sources at 4.10 \leq z \leq 4.35 , monitored by Chandra , and the second is a comparison sample of three sources at 1.33 \leq z \leq 2.74 , monitored by Swift . Together with archival X-ray data , the total rest-frame temporal baseline spans \sim 2 - 4 yr and \sim 5 - 13 yr for the first and second group , respectively . Six of these sources show significant X-ray variability over rest-frame timescales of \sim 10 ^ { 2 } -10 ^ { 3 } d ; three of these also show significant X-ray variability on rest-frame timescales of \sim 1 - 10 d. The X-ray variability properties of our variable sources are similar to those exhibited by nearby and far less luminous active galactic nuclei ( AGNs ) . While we do not directly detect a trend of increasing X-ray variability with redshift , we do confirm previous reports of luminous AGNs exhibiting X-ray variability above that expected from their luminosities , based on simplistic extrapolation from lower luminosity sources . This result may be attributed to luminous sources at the highest redshifts having relatively high accretion rates . Complementary UV-optical monitoring of our sources shows that variations in their optical-X-ray spectral energy distribution are dominated by the X-ray variations . We confirm previous reports of X-ray spectral variations in one of our sources , HS 1700 + 6416 , but do not detect such variations in any of our other sources in spite of X-ray flux variations of up to a factor of \sim 4 . This project is designed to provide a basic assessment of the X-ray variability properties of RQQs at the highest accessible redshifts that will serve as a benchmark for more systematic monitoring of such sources with future X-ray missions .