An optically pumped semiconductor disk laser using submonolayer quantum dots (SML QDs) as gain medium is demonstrated. High-power operation is achieved with stacked InAs/GaAs SML QDs grown by metal-organic vapor-phase epitaxy. Each SML-QD layer is formed from tenfold alternate depositions of nominally 0.5 ML InAs and 2.3 ML GaAs. Resonant periodic gain from a 13-fold nonuniform stack design of SML QDs allows to produce 1.4 W cw at 1034 nm. The disk laser demonstrates the promising potential of SML-QD structures combining properties of QD and quantum-well gain media for high-power applications.