  The interplay between spin frustration and charge fluctuation gives rise to
an exotic quantum state in the intermediate-interaction regime of the
half-filled triangular-lattice Hubbard (TLU) model, while the nature of the
state is under debate. Using the density matrix renormalization group with
SU(2)$_{\rm{spin}} \otimes $U(1)$_{\rm{charge}}$ symmetries implemented, we
study the TLU model defined on the long cylinder geometry with circumference
$W=4$. A gapped quantum spin liquid, with on-site interaction $9 \lesssim U / t
\lesssim 10.75$, is identified between the metallic and the antiferromagnetic
Mott insulating phases. In particular, we find that this spin liquid develops a
robust long-range spin scalar-chiral correlation as the system length $L$
increases, which unambiguously unveils the spontaneous time-reversal symmetry
breaking. In addition, the large degeneracy of the entanglement spectrum
supports symmetry fractionalization and spinon edge modes in the obtained
ground state. The possible origin of chiral order in this intermediate spin
liquid and its relation to the rotonlike excitations have also been discussed.
