The relative fitness of drug-resistant versus susceptible bacteria in an environment dictates resistance prevalence. Estimates for the relative fitness of resistant Mycobacterium tuberculosis (Mtb) strains are highly heterogeneous and mostly derived from in vitro experiments. Measuring fitness in the field allows us to determine how the environment influences the spread of resistance. We designed a household structured, stochastic mathematical model to estimate the fitness costs associated with multidrug resistance (MDR) carriage in Mtb in Lima, Peru during 2010 - 2013. By fitting the model to data from a large prospective cohort study of TB disease in household contacts, we estimated the fitness, relative to susceptible strains with a fitness of 1, of MDR-Mtb to be 0.32 (95% credible interval: 0.15 - 0.62) or 0.38 (0.24 - 0.61), if only transmission or progression to disease, respectively, was affected. The relative fitness of MDR-Mtb increased to 0.56 (0.42 - 0.72) when the fitness cost influenced both transmission and progression to disease equally. We found the average relative fitness of MDR-Mtb circulating within households in Lima, Peru during 2010 - 2013 to be significantly lower than concurrent susceptible Mtb. If these fitness levels do not change, then existing TB control programmes are likely to keep MDR-TB prevalence at current levels in Lima, Peru.