Sea lice threaten the welfare of farmed Atlantic salmon and the sustainability of fish farming across the world. Chemical treatments are the major method of control but drug resistance means that alternatives are urgently needed. Selective breeding can be a cheap and effective alternative. Here, we combine experimental trials and diagnostics to provide a practical protocol for quantifying resistance to sea lice. We then combined quantitative genetics with epidemiological modelling to make the first prediction of the response to selection, quantified in terms of reduced need for chemical treatments. We infected over 1400 young fish with Lepeophtheirus salmonis, the most important species in the Northern Hemisphere. Mechanisms of resistance were expressed early in infection. Consequently, the number of lice per fish and the ranking of families were very similar at 7 and 17 days post infection, providing a stable window for assessing susceptibility to infection. The heritability of lice numbers within this time window was moderately high at 0.3, confirming that selective breeding is viable. We combined an epidemiological model of sea lice infection and control on a salmon farm with genetic variation in susceptibility among individuals. We simulated 10 generations of selective breeding and examined the frequency of treatments needed to control infection. Our model predicted that substantially fewer chemical treatments are needed to control lice outbreaks in selected populations and chemical treatment could be unnecessary after 10 generations of selection. Selective breeding for sea lice resistance should reduce the impact of sea lice on fish health and thus substantially improve the sustainability of Atlantic salmon production.