Prestellar cores are unique laboratories for studying the chemical and physical conditions preceding star formation. We observed the prestellar core L1544 in the fundamental transition of ortho-H 2 D + (1 1,0 -1 1,1 ) at different positions over 100 00 and found a strong correlation between its abundance and the CO depletion factor. We also present a tentative detection of the fundamental transition of para-D 2 H + (1 1,0 -1 0,1 ) at the dust emission peak. Maps in N 2 H + , N 2 D + , HCO + , and DCO + are used and interpreted with the aid of a spherically symmetric chemical model that predicts the column densities and abundances of these species as a function of radius. The correlation between the observed deuterium fractionation of H þ 3 , N 2 H + , and HCO + and the observed integrated CO depletion factor across the core can be reproduced by this chemical model. In addition, a simpler model is used to study the H 2 D + ortho-to-para ratio. We conclude that, in order to reproduce the observed ortho-H 2 D + observations, the grain radius should be larger than 0.3 m.