Adding Si into transition-metal nitride hard coatings is known to enhance mechanical properties and oxidation resistance. At the same time, however, Si promotes precipitation of wurtzite-structure AlN in Ti1-xAlxN during deposition by magnetron sputtering or cathodic-arc-evaporation, resulting in a decrease in layer hardness. Here, we report nanocomposite films of metastable cubic NaCl-structure TiAlSiN deposited using a hybrid approach combining high-power impulse magnetron sputtering (HiPIMS) from an Al target with DC magnetron sputtering (DCMS) from TiSi targets (Al-HiPIMS/TiSi-DCMS) in which a substrate bias is synchronized to the metal-rich portion of each HiPIMS pulse. The Al/(Al + Ti) ratio is varied from 0.26 to 0.77 by adjusting the TiSi target power, while the Si content ranges from 7.6 to 10.3 at.%. Cubic-structure TiAlSiN solid solutions are obtained with a maximum Al/(Al + Ti) atomic ratio of 0.59 and 9.4 at.% Si. Excess Si segregates to grain boundaries to form a SiNx-rich tissue phase. The hardness H and elastic modulus E of cubic TiAlSiN films increase from H = 19.4 +/- 1.7 and E = 322 +/- 12 for TiAlSiN layer with Al/(Al + Ti) = 0.26 to H = 37.3 +/- 1.3 and E = 388 +/- 12 GPa for TiAlSiN layer with Al/(Al + Ti) = 0.59. The TiAlSiN films also exhibit a low intrinsic stress (-0.55 to 0.62 GPa), resulting in a combination of properties: superior hardness and low stress.