  Device-independent (DI) quantum communication will require a loophole-free
violation of Bell inequalities. In typical scenarios where line-of-sight
between the communicating parties is not available, it is convenient to use
energy-time entangled photons due to intrinsic robustness while propagating
over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt
Bell inequality violation with two parties separated by 3.7 km over the
deployed optical fiber network belonging to the University of Concepci\'on in
Chile. Remarkably, this is the first Bell violation with spatially separated
parties that is free of the post-selection loophole, which affected all
previous in-field long-distance energy-time experiments. Our work takes a
further step towards a fiber-based loophole-free Bell test, which is highly
desired for secure quantum communication due to the widespread existing
telecommunication infrastructure.
