Linear compartmental systems are mathematical systems that are frequently used in biology and mathematics. The inputs, states, and outputs of such systems are positive, because they denote amounts or concentrations of material. For linear dynamic systems the observer problem has been solved. The purpose of the observer problem is to determine a linear observer such that the state can be approximated. The difference between the state and its estimate should converge to zero. The interpretation in terms of a physical system requires that an estimate of the state be positive, like the state itself. In this paper conditions on the system matrices are presented that guarantee that there exists a positive linear observer such that both the error converges to zero and the estimate is positive.