  We observe narrowband pairs of time-correlated photons of wavelengths 776\,nm
and 795\,nm from non-degenerate four-wave mixing in a laser-cooled atomic
ensemble of $^{87}${Rb} using a cascade decay scheme. Coupling the photon pairs
into single mode fibers, we observe an instantaneous rate of 7700 pairs per
second with silicon avalanche photodetectors, and an optical bandwidth below
30\,MHz. Detection events exhibit a strong correlation in time
($g^{(2)}(\tau=0)\approx5800$), and a high coupling efficiency indicated by a
pair-to-single ratio of 23%. The violation of the Cauchy-Schwarz inequality by
a factor of $8.4\times10^6$ indicates a strong non-classical correlation
between the generated fields, while a Hanbury--Brown--Twiss experiment in the
individual photons reveals their thermal nature. The narrow bandwidth and
brightness of our source makes it ideal for interacting with atomic ensembles
in quantum communication protocols.
