One promising route towards creating novel topological states and excitations is to combine superconductivity and quantum Hall (QH) effect. It has been predicted that QH chiral edge states can carry supercurrent. However, signatures of superconductivity in the QH regime remain scarce, and a superconducting current through a QH weak link has so far eluded experimental observation. By utilizing high mobility graphene/boron nitride heterostructures we demonstrate the existence of a new type of supercurrent-carrying states in a QH region at magnetic fields as high as 2 Tesla. Ballistic Josephson junctions are made using encapsulated graphene contacted by Mo-Re alloy superconductor resulting in TC=8.5 K and HC2= 8T. At low magnetic fields, devices demonstrate the conventional Fraunhoffer pattern, confirming their uniformity. In the QH regime, when Landau quantization is fully developed, regions of superconductivity can be observed on top of the conventional QH fan diagram. The measured supercurrent is very small, and could be suppressed by applying a DC current of only a few nA through the sample (compare the two panels of the Figure). It is evident that the traditional Andreev bound states cannot exist in the quantum Hall regime, when the bulk of the junction is gapped by the Landau quantization so that a current may only flow along the edges. Indeed, one chiral edge state can only conduct charge carriers (both electrons and holes) in one direction. Therefore, both edges have to be involved to supercurrent between the two contacts. However, edge states with opposite momenta are separated by the width of the junction, which greatly exceeds the coherence length of the MoRe electrodes (a few nanometers). We discuss a novel mechanism that couples the edge states on the opposite sides of the sample through the hybrid electron-hole modes, which are formed at the interfaces between the superconducting contacts and the QH region. The resulting supercurrent is found to be highly periodic in incremental magnetic field applied on top of the quantized field of the order of 1 Tesla, with the typical periodicity of the order of 1mT or less. This periodicity corresponds to the magnetic flux threaded through the area encompassed by the edge states.