The kinetics of the single transition over a fluctuating barrier is ex
amined. The colored noise is approximated by a random telegraph proces
s. The considered process is equivalent to (i) the macroscopic kinetic
s of a simple chemical reaction with fluctuating activation energy, an
d (ii) with the Ornstein-Uhlenbeck process driven by multiplicative di
chotomic noise. The complete solution is found in the form of all mome
nts of the time-dependent probability distribution.