We have constructed a rotating submillikelvin cryostat in which the dilution refrigerator can be operated in a continuous mode using two cryopumps. The4He pot is also equipped with similar pumps. The dilution unit is employed to precool a nuclear stage with 32 mol of copper in an 8-T field. In the design, special care was taken to make fast rotations possible. The apparatus is currently used to measure collective mode phenomena in superfluid3He-B.