In the wake of the renewed interest in multidimensional poverty measurement, a natural question arising is how and whether indices of multidimensional poverty can be adapted to produce measures that quantify both the joint incidence of multiple deprivations and their degree of persistence, i.e. their chronicity. In this paper we seek to build one bridge between these two literatures (on multidimensionality and on poverty dynamics) by proposing indices that are sensitive, simultaneously, to: 1) the number of poverty dimensions in which people are deprived; and 2) the duration of their poverty experience. We propose two families of measures: one that captures multidimensional chronic deprivations (i.e. the joint existence of several dimension-specific chronic poverty experiences), and one that quantifies chronic multidimensional poverty (i.e. the persistence over several periods of contemporaneous multiple deprivations).