This Letter reports the observation of WWW production and a measurement of its cross section using detector at the Large Hadron Collider. Events with two same-sign leptons (electrons or muons) and at least two jets, as well as events with three charged leptons, are selected. A multivariate technique is then used to discriminate between signal and background events. Events from WWW production are observed with a significance of 8.0 standard deviations, where the expectation is 5.4 standard deviations. The inclusive WWW production cross section is measured to be 820 ??? 100 ??stat?? ??? 80 ??syst?? fb, approximately 2.6 standard deviations from the predicted cross section of 511 ??? 18 fb calculated at next-to-leading-order QCD and leading-order electroweak accuracy.