The purpose of this work is to enable risk-limiting electricity dispatch through a market mechanism. There has been a solid body of work on centralized risk-limiting dispatch, which guarantees that the risk of energy shortage is within a user-specified bound. The current trading mechanism of a day-ahead electricity market can be viewed as a market that deals with the expectation (i.e., the first moment) of future supply and load. We show in this paper that distributed and risk-limiting dispatch is enabled by also trading the standard deviation (i.e., the second moment). In the proposed mechanism, a dispatchable power provider, such as spinning reserve and battery, can 'sell' the standard deviation in a market by contributing to absorbing the uncertainty of energy demand and supply. The market-clearing prices of the mean and the standard deviation of electricity are found through the Walrasian auction. This approach allows each power provider to specify the probability density function (pdf) of the amount of energy that it has to generate in the future. As a result, a power provider can quantitatively limit the risk of power shortage by imposing chance constraints in a decentralized manner. The decentralized risk-limiting dispatch and pricing problem are solved at each time step with a receding time horizon. We demonstrate the capabilities of the proposed approach by simulations using real data.