Sensitive X-ray imaging surveys provide a new and effective tool to establish the census of pre-main sequence ( PMS ) stars in nearby young stellar clusters . We report here a deep Chandra X - ray Observatory observation of PMS stars in the Chamaeleon I North cloud , achieving a limiting luminosity of \log L _ { t } \simeq 27 erg s ^ { -1 } ( 0.5 - 8 keV band ) in a 0.8 \times 0.8 pc region . Of the 107 X-ray sources , 37 are associated with Galactic stars of which 27 are previously recognized cloud members . These include three PMS brown dwarfs ; the protostellar brown dwarf ISO 192 has a particularly high level of magnetic activity . Followup optical photometry and spectroscopy establishes that 9-10 of the Chandra sources are probably magnetically active background stars . Several previously proposed cloud members are also inferred to be interlopers due to the absence of X-ray emission at the level expected from the \log L _ { t } - K correlation . No new X-ray discovered stars were confidently found despite the high sensitivity . From these findings , we argue that the sample of 27 PMS cloud members in the Chandra field is uncontaminated and complete down to K = 12 or M \simeq 0.1 M _ { o } dot . The initial mass function ( IMF ) derived from our sample is deficient in 0.1 - 0.3 M _ { \odot } stars compared to the IMF of the rich Orion Nebula Cluster and other Galactic populations . We can not discriminate whether this is due to different star formation processes , mass segregation , or dynamical ejection of lower mass stars .