  The semimetallic or semiconducting nature of the transition metal
dichalcogenide 1$T$-TiSe$_2$ remains under debate after many decades mainly due
to the fluctuating nature of its 2 $\times$ 2 $\times$ 2 charge-density-wave
(CDW) phase at room-temperature. In this letter, using angle-resolved
photoemission spectroscopy, we unambiguously demonstrate that the 1$T$-TiSe$_2$
normal state is semimetallic with an electron-hole band overlap of $\sim$110
meV by probing the low-energy electronic states of the perturbed CDW phase
strongly doped by alkali atoms. Our study not only closes a long-standing
debate but also supports the central role of the Fermi surface for driving the
CDW and superconducting instabilities in 1$T$-TiSe$_2$.
