We consider the problem of how throughput in a wireless network with randomly located nodes scales as the number of users grows. Following the physical model of Gupta and Kumar, we show that randomly scattered nodes can achieve the optimal 1/sqrt(n) per-node transmission rate of arbitrarily located nodes. This contrasts with previous achievable results suggesting that a 1/sqrt(n log(n)) reduced rate is the price to pay for the additional randomness introduced into the system. Of independent interest is that we directly apply results from percolation theory to prove our result.