Herein we present an algorithm for controlling LTI processes using an adaptive sampling interval where the controller at every sampling instant not only computes the new control command but also decides the time interval to the next sample. The approach relies on MPC where the cost function depends on the control performance as well as the cost for sampling. The paper presents a method for synthesizing such a predictive controller and gives explicit conditions for when it is stabilizing. Further it is shown that the optimization problem may be solved off-line and that the controller may be implemented as a lookup table of state feedback gains. The paper is concluded with a numerical example.