We report experimental generation of non-classically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons are separated by a controllable time delay up to 2 microseconds. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.