We experimentally engineer a moatlike dispersion in a system of weakly interacting bosons. By periodically modulating the amplitude of a checkerboard optical lattice, the two lowest isolated bands are hybridized such that the single particle energy displays a continuum of nearly degenerate minima that lie along a circle in reciprocal space. The moatlike structure is confirmed by observing a zero group velocity at nonzero quasimomentum and we directly observe the effect of the modified dispersion on the trajectory of the center of mass position of the condensate. We measure the lifetime of condensates loaded into different moat bands at different quasimomenta and compare to theoretical predictions based on a linear stability analysis of Bogoliubov excitations. We find that the condensate decay increases rapidly as the quasimomentum is decreased below the radius of the moat minimum, and argue that such dynamical instability is characteristic of moatlike dispersions, including spin-orbit coupled systems. The ground state of strongly interacting bosons in such degenerate energy landscapes is expected to be highly correlated, and our work represents a step toward realizing fractional quantum Hall-like states of bosons in an optical lattice.