We consider a narrow magneto-dipole transition in the Tm-169 atom at the wavelength of 1.14 mu m as a candidate for a two-dimensional-optical lattice clock. Calculating dynamic polarizabilities of the two clock levels [Xe]4f(13)6s(2)(J = 7/2) and [Xe]4f(13)6s(2)(J = 5/2) in the spectral range from 250 to 1200 nm, we find a "magic" wavelength for the optical lattice at 807 nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction, and other effects which can perturb the transition frequency are calculated. The transition at 1.14 mu m demonstrates low sensitivity to the BBR shift corresponding to 8 x 10(-17) in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than 5 x 10(-18) in fractional units. By direct excitation of the 1.14 mu m transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level [Xe]4f(13)6s(2) (J = 5/2) of 112 ms which corresponds to a natural spectral linewidth narrower than 1.4 Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at 532 nm.