Materials with high thermal conductivities (κ) are valuable to solve the challenge of waste heat dissipation in highly integrated and miniaturized modern devices. Herein, we report the first synthesis of atomically thin isotopically pure hexagonal boron nitride (BN) and its one of the highest κ among all semiconductors and electric insulators. Single atomic layer (1L) BN enriched with ^{11}B has a κ up to 1009 W/mK at room temperature. We find that the isotope engineering mainly suppresses the out-of-plane optical (ZO) phonon scatterings in BN, which subsequently reduces acoustic-optical scatterings between ZO and transverse acoustic (TA) and longitudinal acoustic phonons. On the other hand, reducing the thickness to a single atomic layer diminishes the interlayer interactions and hence umklapp scatterings of the out-of-plane acoustic (ZA) phonons, though this thickness-induced κ enhancement is not as dramatic as that in naturally occurring BN. With many of its unique properties, atomically thin monoisotopic BN is promising on heat management in van der Waals devices and future flexible electronics. The isotope engineering of atomically thin BN may also open up other appealing applications and opportunities in 2D materials yet to be explored.