YbMgGaO4, a structurally perfect two-dimensional triangular lattice with an odd number of electrons per unit cell and spin-orbit entangled effective spin-1/2 local moments for the Yb(3+) ions, is likely to experimentally realize the quantum spin liquid ground state. We report the first experimental characterization of single-crystal YbMgGaO4 samples. Because of the spin-orbit entanglement, the interaction between the neighboring Yb(3+) moments depends on the bond orientations and is highly anisotropic in the spin space. We carry out thermodynamic and the electron spin resonance measurements to confirm the anisotropic nature of the spin interaction as well as to quantitatively determine the couplings. Our result is a first step towards the theoretical understanding of the possible quantum spin liquid ground state in this system and sheds new light on the search for quantum spin liquids in strong spin-orbit coupled insulators.