In this paper we make welfare comparisons among districts of Zambia using multidimensional wellbeing indicators observed at the household level. The comparisons are conducted using a first order dominance approach developed by Arndt et al. (2012). It is assumed that the levels of deprivation for each indicator can be ranked ordinally from worse to better. The ranking is done without making any assumptions about the relative importance of any of the indicators. This approach is applied to the 2010 Census of Population and Housing data. The analysis has generated information on the poverty status of provinces and districts in Zambia and has ranked them from the relatively well off to the worse off. This information has been presented on a map showing the districts according to their poverty status. It is expected that this paper will contribute to fine tuning geographic poverty targeting efforts in Zambia. The rationale is that with the availability of such analysis, it will be possible to make budgetary provisions that allow for the equitable distribution of public resources. The overriding objective of the government should be to channel public resources based on the spatial distribution of poverty.