Despite of poverty and extreme poverty estimations having decreased during the period 2006–2016 in Peru, from 49.1 to 20.7% and from 16.1 to 3.8%, respectively, the poor population still represents a latent concern for policy makers. Essentially, the main reason lies on the multidimensional problems of quality of life. Then, a research question yet unaddressed rises: Is it possible to find very poor people who feel happy? If so, what controls this relationship? The first main contribution of this study is the application of modern measurement theory to measure happiness. The short Oxford Happiness Questionnaire jointly with an ad hoc Multidimensional Poverty Index-MPI (8 items) were applied to a random sample of 537 household heads who live in the five poorest districts in Peru. Item response theory analysis was conducted to measure happiness scores. Findings reveal happiness scores and the MPI are negatively associated in the very poor Peru. Friendship, religiosity, and some relevant non-material characteristics of a family are the most important covariates of the relationship between these variables. In fact, the second contribution of this study represents the inclusion of variables associated to the quantity and quality of friendship as relevant controllers of happiness and poverty.