  G21.5-0.9 is a plerionic supernova remnant (SNR) whose properties hint at the
presence of a pulsar -- yet no pulsations have been found at any wavelength.
Early observations with Chandra led to the discovery of an extended component,
making the SNR at least twice as big as originally thought. Our analysis
indicates that this low-surface brightness extended component is non-thermal.
We perform a spatially resolved spectroscopy using a 72 ksec exposure with
ACIS-S, and find no evidence of line emission. The 5-arcminute diameter remnant
is well fitted with a power law with a photon index steepening from 1.5
(central core) to 2.7 (extended component) and a column density N_H=2.2 10^22
cm^-2. Using a 76 ksec exposure with the HRC, we derive an upper limit of 16%
on the pulsed fraction from a putative pulsar. We also infer the parameters of
the `hidden pulsar' in G21.5-0.9 in comparison with the Crab and 3C 58 pulsars.
This remnant remains unique and intriguing since it is, to date, the only
candidate whose size is bigger in X-rays than in the radio.
