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$.
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