Optical nanoantennas are capable of enhancing the near-field intensity and confining optical energy within a small spot size. We report a novel metal-dielectric-metal coupled-nanorods antenna integrated on the facet of a quantum-cascade laser. Finite-difference time-domain simulations showed that, for dielectric thicknesses in the range from 10 to 30 nm, peak optical intensity at the top of the antenna gap is 4000 times greater than the incident field intensity. This is 4 times higher enhancement compared to a coupled metal antenna. The antenna is fabricated using focused ion-beam milling and measured using modified scanning probe microscopy. Such a device has potential applications in building mid-IR biosensors.