The heating of the chromosphere is a long-lived puzzle in modern astronomy. Solar synoptic maps of He I 10830 angstrom intensity, which are observed at National Solar Observatory/Kitt Peak from Jul. 2005 to Mar. 2013 are utilized to investigate the phase relation of long-term evolution of the quiet chromosphere represented by He I intensity with the solar cycle represented by sunspot number. The phase relationship of the He I chromosphere at low and middle latitudes with the solar cycle is found to show an interesting phenomenon, black under the light: (1) at most of the latitudes of the conspicuous active chromosphere (the butterfly diagram), the relationship is anti-phase, but at the latitudes outside the butterfly diagram (the inconspicuous background chromosphere), it is in-phase; and (2) the He I intensity averaged over the low latitudes of 0-30 degrees is in anti-phase with the solar cycle, but after deducing some relatively small values of He I intensity, the anti-phase relationship is reversed to be in-phase. Long-term variation of He I intensity at the full disk of the quiet chromosphere is believed to be in phase with the solar cycle, and accordingly, the temporal evolution of the heated quiet chromosphere is in phase with long-term variation of the small-scale magnetic elements whose flux is (2.9 - 32.0)x10(18) Mx, and it provides evidence for the heating of the quiet chromosphere mainly by the magnetic elements. Implication of the findings is discussed, and especially, the long-term variation of total solar irradiance measured at low latitudes is inferred to be significantly different from that at high latitudes.