In the past two decades, deeply virtual Compton scattering of electrons has been successfully used to advance our knowledge of the partonic structure of the free proton and investigate correlations between the transverse position and the longitudinal momentum of quarks inside the nucleon. Meanwhile, the structure of bound nucleons in nuclei has been studied in inclusive deep-inelastic lepton scattering experiments off nuclear targets, showing a significant difference in longitudinal momentum distribution of quarks inside the bound nucleon, known as the EMC effect. In this Letter, we report the first beam spin asymmetry (BSA) measurement of exclusive deeply virtual Compton scattering off a proton bound in 4He. The data used here were accumul...