We study the optimal stopping problem proposed by Dupuis and Wang in . In this maximiza- tion problem of expected present value of exercise payo?, the underlying dynamics follow a linear diffusion. The decision maker is not allowed to stop at any time she chooses but rather on the jump times of an independent Poisson process. In , the authors solve this problem in the case where the underlying is a geometric Brownian motion and the payoff function is of American call option type. In the current study, we propose a mild set of conditions (covering the setup of ) on both the underlying and the payoff and build and use a Markovian apparatus based on the Bellman principle of optimality to solve the problem under these conditions. We also discuss interpretation of this model as optimal timing of an irreversible investment decision under an exogenous information constraint.