Because of inversion symmetry and particle exchange, all constituents of homonuclear diatomic molecules are in a quantum mechanically non-local coherent state; this includes the nuclei and deep-lying core electrons. Hence, the molecular photoemission can be regarded as a natural double-slit experiment: coherent electron emission originates from two identical sites, and should give rise to characteristic interference patterns. However, the quantum coherence is obscured if the two possible symmetry states of the electronic wavefunction ('gerade' and 'ungerade') are degenerate; the sum of the two exactly resembles the distinguishable, incoherent emission from two localized core sites. Here we observe the coherence of core electrons in N(2) through a direct measurement of the interference exhibited in their emission. We also explore the gradual transition to a symmetry-broken system of localized electrons by comparing different isotope-substituted species--a phenomenon analogous to the acquisition of partial 'which-way' information in macroscopic double-slit experiments.