Exoplanetary science has reached a historic moment. The James Webb Space Telescope will be capable of probing the atmospheres of rocky planets, and perhaps even search for biologically produced gases. However this is contingent on identifying suitable targets before the end of the mission. A race therefore, is on, to find transiting planets with the most favorable properties, in time for the launch. Here, we describe a realistic opportunity to discover extremely favorable targets - rocky planets transiting nearby brown dwarfs - using the Spitzer Space Telescope as a survey instrument. Harnessing the continuous time coverage and the exquisite precision of Spitzer in a 5,400 hour campaign monitoring nearby brown dwarfs, we will detect a handful of planetary systems with planets as small as Mars. The survey we envision is a logical extension of the immense progress that has been realized in the field of exoplanets and a natural outcome of the exploration of the solar neighborhood to map where the nearest habitable rocky planets are located (as advocated by the 2010 Decadal Survey). Our program represents an essential step towards the atmospheric characterization of terrestrial planets and carries the compelling promise of studying the concept of habitability beyond Earth-like conditions. In addition, our photometric monitoring will provide invaluable observations of a large sample of nearby brown dwarfs situated close to the M/L transition. This is why, we also advocate an immediate public release of the survey data, to guarantee rapid progress on the planet search and provide a treasure trove of data for brown dwarf science.< Réduire