The objective of this paper is to investigate whether, in a Sidrauski type model with uncertainty, welfare maximization calls for following the famous "Chicago Rule". This question will be answered in the affirmative in this paper, i.e. social welfare optimization calls for a zero nominal interest rate on one-period bonds. The zero nominal interest rate, however, does not imply in an uncertain world that there is no systematic difference between the expected rate of deflation and the rate of time preference in an economy without growth. The magnitude of this difference turns out to be small, however. Numerical welfare comparisons are made between the optimal policy and policies in which the growth rate of money is fixed. The optimal policy requires that the monetary authorities react every period to the available information and they choose a growth level of the money stock that will set the interest rate equal to zero. If we compare the time paths of the real variables under the optimal policy with the time paths if the money supply decreases at a rate equal to the rate of time preference, then we see hardly any differences. The price dynamics can be very different, however. The paper also investigates the issue of superneutrality and finds that the quantitative deviations from superneutrality are substantial if a model with a shopping time technology is used. The neo-classical models in this paper are solved numerically using a technique developed in Marcet (1988).