The Barnard 1b core shows signatures of being at the earliest stages of low-mass star formation, with two extremely young and deeply embedded protostellar objects. Hence, this core is an ideal target to study the structure and chemistry of the first objects formed in the collapse of prestellar cores. We present ALMA Band 6 spectral line observations at ~0.6'' of angular resolution towards Barnard 1b. We have extracted the spectra towards both protostars, and used a Local Thermodynamic Equilibrium (LTE) model to reproduce the observed line profiles. B1b-S shows rich and complex spectra, with emission from high energy transitions of complex molecules, such as CH3OCOH and CH3CHO, including vibrational level transitions. We have tentatively detected for the first time in this source emission from NH2CN, NH2CHO, CH3CH2OH, CH2OHCHO, CH3CH2OCOH and both aGg' and gGg' conformers of (CH2OH)2. This is the first detection of ethyl formate (CH3CH2OCOH) towards a low-mass star forming region. On the other hand, the spectra of the FHSC candidate B1b-N are free of COMs emission. In order to fit the observed line profiles in B1b-S, we used a source model with two components: an inner hot and compact component (200 K, 0.35'') and an outer and colder one (60 K, 0.6''). The resulting COM abundances in B1b-S range from 1e-13 for NH2CN and NH2CHO, up to 1e-9 for CH3OCOH. Our ALMA Band 6 observations reveal the presence of a compact and hot component in B1b-S, with moderate abundances of complex organics. These results indicate that a hot corino is being formed in this very young Class 0 source.