In this work we derive an easily testable sufficient condition for assessing almost sure (AS) stability of a continuous-time Markov jump linear system (MJLS) with a finite state Markov form process. Such a condition is used to design a feedback stabilization strategy under the hypothesis that at least one mode is controllable. The proposed condition relies on some bounds on the 2-norm of the transition matrix over the time interval to the first jump. Such bounds are computed from the eigenvalues of the solutions of a set of associated Lyapunov equations, one for each mode. An algorithm is also given for designing the stabilizing feedback, based on a formulation of the sufficient condition in terms of an equivalent LMI problem