Inspired by the groundbreaking discovery of the 2H-MoS2 monolayer with outstanding physical properties, the electronic structure, structural stability, and thermal transport of 2H-CrX2 (X = S and Se) monolayers are theoretically evaluated using density functional theory (DFT) calculations and semiempirical Boltzmann transport theory. The 2H-CrX2 (X = S and Se) monolayers are direct semiconductors with the bandgaps of 0.91 and 0.69 eV. The elastic modulus and phonon dispersion curve analysis show that the 2H-CrX2 (X = S and Se) monolayers possess excellent mechanical and dynamic stabilities on account of elastic constants satisfying the Born-Huang criterion and the absence of negative frequencies. The thermal stabilities of the 2H-CrX2 (X = S and Se) monolayers at 300 K are proved by ab initio molecular dynamics (AIMD) simulations, as evidenced by the slight changes in the structural evolution and small fluctuation in total energy. High thermal conductivities of 131.7 and 88.6 W m-1 K-1 are discovered for 2H-CrS2 and 2H-CrSe2 monolayers at 300 K. Further analysis of the phonon group velocity, phonon relaxation time, and Grüneisen parameter shows that the high lattice thermal conductivities of 2H-CrX2 (X = S and Se) monolayers could be attributed to the great bond strength, large Young's modulus, relatively small atomic mass, high phonon group velocity, and long phonon relaxation time. In addition, the various scattering mechanisms are further considered in the calculations of phonon thermal transport to evaluate the effect of the scattering rates of the 2H-CrS2 and 2H-CrSe2 monolayers on the lattice thermal conductivity, and the determinative role is found for the phonon boundary scattering. Our present study would not only offer a fundamental understanding of the thermal transport properties of the 2H-CrX2 (X = S and Se) monolayers, but also provide theoretical guidelines for the experimental investigation of thermal management materials with 2H-phase.