We study a real-time sampling problem: Samples of a Wiener process (our signal model) are taken and forwarded to a remote estimator via a channel with random delay; the estimator forms a real-time estimate of the signal from causally received samples. The optimal sampling policy for minimizing the MMSE subject to a sampling-rate constraint is obtained exactly, which is determined by the signal, sampler, and channel in a simple form. When the sampling times are independent of the observed signal, this problem reduces to an Age-of-Information optimization problem. Extensions to stationary Gauss-Markov signals (i.e., the Ornstein-Uhlenbeck process) will be also discussed.