Electron-capture delayed fission was observed in {sup 244}Es produced via the {sup 237}Np({sup 12}C,5n){sup 244}Es reaction at 81 MeV (on target) with a production cross section of 0.31{+-}0.12 {micro}b. The mass-yield distribution of the fission fragments is highly asymmetric. The average preneutron-emission total kinetic energy of the fragments was measured to be 186{+-}19 MeV. Based on the ratio of the number of fission events to the measured number of {alpha} decays from the electron-capture daughter {sup 244}Cf (100% {alpha} branch), the probability of delayed fission was determined to be (1.2{+-}0.4) x 10{sup -4}. This value for the delayed fission probability fits the experimentally observed trend of increasing delayed fission probability with increasing Q value for electron-capture.