Planet formation theories predict a large but still undetected population of short-period terrestrial planets orbiting brown dwarfs . Should specimens of this population be discovered transiting relatively bright and nearby brown dwarfs , the Jupiter-size and the low luminosity of their hosts would make them exquisite targets for detailed atmospheric characterisation with JWST and future ground-based facilities . The eventual discovery and detailed study of a significant sample of transiting terrestrial planets orbiting nearby brown dwarfs could prove to be useful not only for comparative exoplanetology but also for astrobiology , by bringing us key information on the physical requirements and timescale for the emergence of life . In this context , we present a search for transit-signals in archival time-series photometry acquired by the Spitzer Space Telescope for a sample of 44 nearby brown dwarfs . While these 44 targets were not particularly selected for their brightness , the high precision of their Spitzer light curves allows us to reach sensitivities below Earth-sized planets for 75 % of the sample and down to Europa-sized planets on the brighter targets . We could not identify any unambiguous planetary signal . Instead , we could compute the first limits on the presence of planets on close-in orbits . We find that within a 1.28 day orbit , the occurrence rate of planets with a radius between 0.75 and 3.25 R _ { \oplus } is \eta < 67 \pm 1 \% . For planets with radii between 0.75 and 1.25 R _ { \oplus } , we place a 95 % confident upper limit of \eta < 87 \pm 3 \% . If we assume an occurrence rate of \eta = 27 \% for these planets with radii between 0.75 and 1.25 R _ { \oplus } , as the discoveries of the Kepler-42b and TRAPPIST-1b systems would suggest , we estimate that 175 brown dwarfs need to be monitored in order to guarantee ( 95 % ) at least one detection .