  We detected X-ray emission from PSR B1800-21 and its synchrotron nebula with
the Chandra X-ray Observatory. The pulsar's observed flux is (1.4+/-0.2)
10^{-14} ergs cm^{-2} s^{-1} in the 1-6 keV band. The spectrum can be described
by a two-component PL+BB model, suggesting a mixture of thermal and
magnetospheric emission. For a plausible hydrogen column density n_{H}=1.4
10^{22} cm^{-2}, the PL component has a slope Gamma=1.4+/-0.6 and a luminosity
L_{psr}^{nonth}=4 10^{31}(d/4 kpc)^2 ergs s^{-1}. The properties of the thermal
component (kT=0.1-0.3 keV, L^{bol}=10^{31}-10^{33} ergs s^{-1}) are very poorly
constrained because of the strong interstellar absorption. The compact,
7''\times4'', inner pulsar-wind nebula (PWN), elongated perpendicular to the
pulsar's proper motion, is immersed in a fainter asymmetric emission. The
observed flux of the PWN is (5.5+/-0.6) 10^{-14} ergs cm^{-2} s^{-1} in the 1-8
keV band. The PWN spectrum fits by a PL model with Gamma=1.6+/-0.3, L=1.6
10^{32} (d/4 kpc})^2 ergs s^{-1}. The shape of the inner PWN suggests that the
pulsar moves subsonically and X-ray emission emerges from a torus associated
with the termination shock in the equatorial pulsar wind. The inferred
PWN-pulsar properties (e.g., the PWN X-ray efficiency, L_{pwn}/\dot{E}~10^{-4};
the luminosity ratio, L_{pwn}/L_{psr}^{nonth}=4; the pulsar wind pressure at
the termination shock, p_s=10^{-9} ergs cm^{-3}) are very similar to those of
other subsonically moving Vela-like objects detected with Chandra
(L_{pwn}/\dot{E}=10^{-4.5}-10^{-3.5}, L_{pwn}/L_{psr}^{nonth}~5,
p_s=10^{-10}-10^{-8} ergs cm^{-1}).
