Intersubband transitions in n-doped semiconductor heterostructures allow one to quantum-engineer one of the largest known nonlinear response in condensed matter systems but only for the electric field polarized normal to semiconductor layer. By coupling of a quantum-engineered multi-quantum-well semiconductor layer with electromagnetically-engineered plasmonic elements we may produce ultrathin metasurfaces with giant nonlinear response. Here we experimentally demonstrate metasurfaces designed for second harmonic generation at λ≈9.9 μm with a record-high nonlinear response for condensed-matter systems in infrared/visible spectral range, up to 1.17×106 pm/V. The practical impact of the nonlinear metasurfaces proposed here may be extended to a variety of fields, including THz generation and detection, phase conjugation, and other nonlinear optical processes.