High-harmonic emission from crystalline silicon can be made ten times brighter by exploiting local plasmonic fields in arrays of nano-antennas. Plasmonic antennas can enhance the intensity of a nanojoule laser pulse by localizing the electric field in their proximity1. It has been proposed that the field can become strong enough to convert the fundamental laser frequency into high-order harmonics through an extremely nonlinear interaction with gas atoms that occupy the nanoscopic volume surrounding the antennas2,3,4. However, the small number of gas atoms that can occupy this volume limits the generation of high harmonics5,6,7. Here we use an array of monopole nano-antennas to demonstrate plasmon-assisted high-harmonic generation directly from the supporting crystalline silicon substrate. The high density of the substrate compared with a gas allows macroscopic buildup of harmonic emission. Despite the sparse coverage of antennas on the surface, harmonic emission is ten times brighter than without antennas. Imaging the high-harmonic radiation will allow nanometre and attosecond measurement of the plasmonic field8 thereby enabling more sensitive plasmon sensors9 while opening a new path to extreme-ultraviolet-frequency combs10.