Very young late-type dwarfs at distances closer than 30 pc are excellent sites to provide a direct detection of extrasolar planets. The combination of youth and proximity makes feasible the detection of giant planets of 1-5 Jovian masses orbiting at several astronomical units from the star. According to current models, giant planets with masses 1 to 5 M_Jup and age of 100 Myr may have absolute magnitudes M_J, M_H 19-24, much brighter {by 5-10 mags} than at the age of the Sun. Such short ages, therefore, substantially increase their detectability. We propose to use the NICMOS coronagraph to search for substellar objects around six stars with likely ages of 100 Myr or younger which are located within 30 pc of the Sun. Companions with DeltaH=10-13 mag can be detected at angular separations as close as 0.5 arcsecs, implying in the case of our two nearest stars physical separations of 4-5 AU. Much fainter ones can be detected at larger separations. Our choice of NICMOS filters will provide key information on the surface temperature of any detected substellar object.