  The quantum "mystery which cannot go away" (in Feynman's words) of
wave-particle duality is illustrated in a striking way by Wheeler's
delayed-choice GedankenExperiment. In this experiment, the configuration of a
two-path interferometer is chosen after a single-photon pulse has entered it :
either the interferometer is \textit{closed} (\textit{i.e.} the two paths are
recombined) and the interference is observed, or the interferometer remains
\textit{open} and the path followed by the photon is measured. We report an
almost ideal realization of that GedankenExperiment, where the light pulses are
true single photons, allowing unambiguous which-way measurements, and the
interferometer, which has two spatially separated paths, produces high
visibility interference. The choice between measuring either the 'open' or
'closed' configuration is made by a quantum random number generator, and is
space-like separated -- in the relativistic sense -- from the entering of the
photon into the interferometer. Measurements in the closed configuration show
interference with a visibility of 94%, while measurements in the open
configuration allow us to determine the followed path with an error probability
lower than 1%.
