The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M.P. Zaletel, and J.E. Moore, Phys. Rev. X ${bf 10}$, 021042 (2020)]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider $N$-leg cylinders. In highly-frustrated cases, i.e., in the presence of a next-nearest neighbor hopping with $N=4$, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for the less frustrated case with $N=6$, the chiral spin liquid is not the state with the lowest variational energy and the results are very similar to the one obtained on two-dimensional clusters [L.F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B ${bf 102}$, 115150 (2020)].
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