We present X-ray observations of the BL Lacertae ( BL Lac ) object Markarian 501 ( Mrk 501 ) , taken with the Rossi X-ray Timing Explorer in 1998 May as part of a multi-wavelength campaign .
The X-ray light curve shows a very rapid flare in which the 2-10 keV flux increased by \sim 60 % in < 200 seconds .
This rapid rise is followed by a drop-off in the 2-10 keV flux of \sim 40 % in < 600 seconds .
The 10-15 keV variation in this flare is roughly a factor of two on similar time-scales .
During the rise of the flare , the 3-15 keV spectral index hardened from 2.02 \pm 0.03 to 1.87 \pm 0.04 , where it remained during the decay of the flare .
This is the fastest variation ever seen in X-rays from Mrk 501 and among the fastest seen at any wavelength for this object .
The shift in the energy at which the spectral power peaks ( from \lesssim 3 keV before the flare to / gtrsim 30 keV during the flare ) is also among the most rapid shifts seen from this object .
This flare occurs during an emission state ( 2-10 keV flux \approx 1.2 \times 10 ^ { -10 } erg cm ^ { -2 } s ^ { -1 } ) that is approximately 25 % of the peak flux observed in 1997 April from this object but which is still high compared to its historical average X-ray flux .
The variations in the hardness ratio are consistent with the low energy variations leading those at high energies during the development and decay of the flare .
This pattern is rare among high frequency peaked BL Lac objects like Mrk 501 , but has been seen recently in two other TeV emitting BL Lacs , Mrk 421 and PKS 2155-304 .
The hard lag is consistent with a flare dominated by the acceleration time-scale for a simple relativistic shock model of flaring .