Graphene, a single layer of graphite, has recently attracted considerable attention owing to its remarkable electronic and structural properties and its possible applications in many emerging areas such as graphene-based electronic devices. The charge carriers in graphene behave like massless Dirac fermions, and graphene shows ballistic charge transport, turning it into an ideal material for circuit fabrication. However, graphene lacks a bandgap around the Fermi level, which is the defining concept for semiconductor materials and essential for controlling the conductivity by electronic means. Theory predicts that a tunable bandgap may be engineered by periodic modulations of the graphene lattice, but experimental evidence for this is so far lacking. Here, we demonstrate the existence of a bandgap opening in graphene, induced by the patterned adsorption of atomic hydrogen onto the Moiré superlattice positions of graphene grown on an Ir(111) substrate.