In this paper we consider optimal parameter estimation with a constrained packet transmission rate. Due to the limited battery power and the traffic congestion over a large sensor network, each sensor is required to discard some packets and save transmission times. We propose a packet-driven sensor scheduling policy such that the sensor transmits only the important measurements to the estimator. Unlike the existing deterministic scheduler in [1], our stochastic packet scheduling is novelly designed to maintain the computational simplicity of the resulting maximum-likelihood estimator (MLE). This results in a nice feature that the MLE is still able to be recursively computed in a closed form, and the Cramér-Rao lower bound (CRLB) can be explicitly evaluated. Moreover, an optimization problem is formulated and solved to obtain the optimal parameters of the scheduling policy under which the estimation performance is comparable to the standard MLE (with full measurements) even with a moderate transmission rate. Numerical simulations are included to show the effectiveness.