Spatial distributions of temperature, major species, and OH mole fractions under moderate or intense low-oxygen-dilution (MILD) conditions in a laminar-jet-in-hot-coflow configuration were measured using spontaneous Raman and laser-induced-fluorescence methods. A preheated mixture of 18% CH4/82% N-2 at 1100 K was used as fuel, while the products of a laminar, flat, premixed burner-stabilized flame with an equivalence ratio of 0.8 at 1550 K were used as the oxidizer. For comparison, experiments replacing the fuel by pure N-2 were also performed. The measurements are compared with the results of numerical simulations performed using the GRI-Mech 3.0 chemical mechanism and a multicomponent mixture-averaged transport model. Analysis of the data shows that the maximum axial and radial temperature and OH mole fraction occur on the lean side of the stoichiometric mixture fraction. MILD combustion generates maximum OH mole fractions of similar to 700 ppm in the radial profiles close to the burner exit and similar to 300 ppm along the centerline, more than five times lower than those measured in equivalent methane/air diffusion flames. Overall, good qualitative and quantitative agreement is found between the results of detailed computations and experiments, with the maximum differences observed in the axial OH profiles, which are just outside the estimated experimental uncertainty. Analysis of the computational results shows that differential diffusion hinders the use of the mixture fraction to estimate the equilibrium temperature and species fractions, causing an overestimation of the stoichiometric temperature by similar to 200 K. Calculating the equilibrium quantities based on the local (computed) species fractions shows an axial temperature profile that differs from that experimentally/computationally determined by less than 25 K. The analysis further shows that the measured OH mole fractions are roughly three times higher than the (locally determined) equilibrium value.