In addition to its exotic electronic properties graphene exhibits unusually high intrinsic thermal conductivity. The physics of phonons--the main heat carriers in graphene--has been shown to be substantially different in two-dimensional (2D) crystals, such as graphene, from in three-dimensional (3D) graphite. Here, we report our experimental study of the isotope effects on the thermal properties of graphene. Isotopically modified graphene containing various percentages of 13C were synthesized by chemical vapour deposition (CVD). The regions of different isotopic compositions were parts of the same graphene sheet to ensure uniformity in material parameters. The thermal conductivity, K, of isotopically pure 12C (0.01% 13C) graphene determined by the optothermal Raman technique, was higher than 4,000 W mK(-1) at the measured temperature T(m)~320 K, and more than a factor of two higher than the value of K in graphene sheets composed of a 50:50 mixture of 12C and 13C. The experimental data agree well with our molecular dynamics (MD) simulations, corrected for the long-wavelength phonon contributions by means of the Klemens model. The experimental results are expected to stimulate further studies aimed at a better understanding of thermal phenomena in 2D crystals.