  We have found an exact expression for the decoherence rate of a Josephson
charge qubit coupled to fluctuating background charges. At low temperatures $T$
the decoherence rate ${\Gamma}$ is linear in $T$ while at high temperatures it
saturates in agreement with a known classical solution which, however, reached
at surprisingly high $T$. In contrast to the classical picture, impurity states
spread in a wide interval of energies ($\gg T$) may essentially contribute to
${\Gamma}$.
