We address the problem of observing a linear system dot x = Ax by a scalar polynomial output function. We show that if the null space of A has dimension at most one, then one can always find such an output function which observes the system and when all the eigenvalues of A are real, then a necessary condition for the observability of the system is that the degree of the polynomial is greater than a certain integer which is related to the maximum number of Jordan blocks corresponding to any eigenvalue.