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 \pm 3 % of the total X-ray flux of the pulsar . The Gaussian width of the sharp X-ray peak is 34 \pm 3 \mu s in time , implying a size of the X-ray beam as it crosses the line of sight of 4.0 \pm 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 Nançay , we find the absolute phases in the X-ray wander with respect to this radio ephemeris by up to 60 \mu s , 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 \pm 12 \mu s. We limit the amount of linear drift in the relative timing accuracy of HRC-S to < 3 \times 10 ^ { -10 } s s ^ { -1 } .