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We investigate the low temperature (T < 2 K) electronic structure of the heavy fermion superconductor CeCoIn₅ (T-c = 2.3 K) by angle- resolved photoemission spectroscopy (ARPES). The hybridization between conduction electrons and f electrons, which ultimately leads to the emergence of heavy quasiparticles responsible for the various unusual properties of such materials, is directly monitored and shown to be strongly band dependent. In particular the most two-dimensional band is found to be the least hybridized one. A simplified multiband version of the periodic Anderson model (PAM) is used to describe the data, resulting in semiquantitative agreement with previous bulk sensitive results from de Haas-van Alphen measurements.