  We perform absolute timing of PSR B1821-24 in M28, using a 50 ksec
observation with Chandra/HRC-S. We have obtained the highest signal-to-noise
X-ray pulsed lightcurve of this source to date, detecting two X-ray pulses, as
well as significant non-pulsed emission -- a persistent X-ray flux which
comprises 15+/-3% of the total X-ray flux of the pulsar. The Gaussian width of
the sharp X-ray peak is 34+/-3 micro-sec in time, implying a size of the X-ray
beam as it crosses the line of sight of 4.0+/-0.4 deg. We find evidence for a
significant trailing component in both X-ray peaks of the pulse profile.
Including three RXTE/PCA observations in our analysis, and tying the phases
together using a radio ephemeris obtained at Nancay, we find the absolute
phases in the X-ray wander with respect to this radio ephemeris by up to 60
micro-sec, likely due to the variable dispersion measure, which changes the
pulse arrival time in the radio band but not the X-ray band. The present
analysis makes clear that study of pulsar timing noise properties in
millisecond pulsars such as PSR B1821-24 -- hitherto only studied at radio
wavelengths, where variable dispersion measure requires a significant
correction -- can be studied at X-ray wavelengths, where the effect of variable
dispersion measure is negligible. We also examine the known uncertainties in
the absolute Chandra/HRC-S timing accuracy, which amount to +/-12 microsec. We
limit the amount of linear drift in the relative timing accuracy of HRC-S to
<3e-10 s s-1.
