  Liquid scintillator detectors play a central role in the detection of
neutrinos from various sources. In particular, it is the only technique used so
far for the precision spectroscopy of sub-MeV solar neutrinos, as demonstrated
by the Borexino experiment at the Gran Sasso National Laboratory in Italy. The
benefit of a high light yield, and thus a low energy threshold and a good
energy resolution, comes at the cost of the directional information featured by
water Cherenkov detectors, measuring $^8$B solar neutrinos above a few MeV. In
this paper we provide the first directionality measurement of sub-MeV solar
neutrinos which exploits the correlation between the first few detected photons
in each event and the known position of the Sun for each event. This is also
the first signature of directionality in neutrinos elastically scattering off
electrons in a liquid scintillator target. This measurement exploits the
sub-dominant, fast Cherenkov light emission that precedes the dominant yet
slower scintillation light signal. Through this measurement, we have also been
able to extract the rate of $^{7}$Be solar neutrinos in Borexino. The
demonstration of directional sensitivity in a traditional liquid scintillator
target paves the way for the possible exploitation of the Cherenkov light
signal in future kton-scale experiments using liquid scintillator targets.
Directionality is important for background suppression as well as the
disentanglement of signals from various sources.
