We introduce a hybrid organic-inorganic system consisting of epitaxial NaYF4:Yb3+/X3+@NaYbF4@NaYF4:Nd3+ (X = null, Er, Ho, Tm, or Pr) core/shell/shell (CSS) nanocrystal with organic dye, indocyanine green (ICG) on the nanocrystal surface. This system is able to produce a set of narrow band emissions with a large Stokes-shift (>200 nm) in the second biological window of optical transparency (NIR-II, 1000-1700 nm), by directional energy transfer from light-harvesting surface ICG, via lanthanide ions in the shells, to the emitter X3+ in the core. Surface ICG not only increases the NIR-II emission intensity of inorganic CSS nanocrystals by similar to 4-fold but also provides a broadly excitable spectral range (700-860 nm) that facilitates their use in bioapplications. We show that the NIR-II emission from ICG-sensitized Er3+-doped CSS nanocrystals allows clear observation of a sharp image through 9 mm thick chicken breast tissue, and emission signal detection through 22 mm thick tissue yielding a better imaging profile than from typically used Yb/Tm-codoped upconverting nanocrystals imaged in the NIR-I region (700-950 nm). Our result on in vivo imaging suggests that these ICG-sensitized CSS nanocrystals are suitable for deep optical imaging in the NIR-II region.