We consider a practical ad hoc network where the channel gains from the transmitters to the receivers are only known through their mean and covariance rather than complete distribution functions. Our goal is to minimize the weighted sum of transmission powers with certain throughput guarantees. Under such limited channel state information (due to channel uncertainty), we exploit chance-constrained programming (CCP), which allows occasional violation of throughput threshold as long as the probability of such violation is below a small tolerable constant (risk level). We show that by setting different risk levels, we are able to achieve a trade-off between controlled throughput violation (risk) and minimum power consumption in the network. Through extensive simulations, we show that our proposed solution is significantly better than conventional worst-case optimization (with no risk tolerance) in terms of feasibility and objective value.