  We present an exact solution for a catalytically-activated annihilation A + A
\to 0 reaction taking place on a one-dimensional chain in which some segments
(placed at random, with mean concentration p) possess special, catalytic
properties. Annihilation reaction takes place, as soon as any two A particles
land from the reservoir onto two vacant sites at the extremities of the
catalytic segment, or when any A particle lands onto a vacant site on a
catalytic segment while the site at the other extremity of this segment is
already occupied by another A particle. We find that the disorder-average
pressure $P^{(quen)}$ per site of such a chain is given by $P^{(quen)} =
P^{(lan)} + \beta^{-1} F$, where $P^{(lan)} = \beta^{-1} \ln(1+z)$ is the
Langmuir adsorption pressure, (z being the activity and \beta^{-1} - the
temperature), while $\beta^{-1} F$ is the reaction-induced contribution, which
can be expressed, under appropriate change of notations, as the Lyapunov
exponent for the product of 2 \times 2 random matrices, obtained exactly by
Derrida and Hilhorst (J. Phys. A {\bf 16}, 2641 (1983)). Explicit asymptotic
formulae for the particle mean density and the compressibility are also
presented.
