In a network of neuronal oscillators with time-delayed coupling, we uncover a phenomenon of enhancement of neural synchrony by time delay: a stable synchronized state exists at low coupling strengths for significant time delays. By formulating a master stability equation for time-delayed networks of Hindmarsh-Rose neurons, we show that there is always an extended region of stable synchronous activity corresponding to low coupling strengths. Such synchrony could be achieved in the undelayed system only by much higher coupling strengths. This phenomenon of enhanced neural synchrony by delay has important implications, in particular, in understanding synchronization of distant neurons and information processing in the brain.,