Boron-rich boron carbide (B4.9C) single crystals are prepared by laser diode floating zone method and their anisotropic mechanical response is investigated using nanoindentation. A Berkovich indenter is used to perform indentations over a depth range of ~100 nm to ~1 m on four single crystal regions with a surface normal of (1-322), (6-3-34), (41-57), or (1-21,14). For each single crystal, in-plane variations of indentation modulus and hardness is also studied by monitoring the relative orientation between the crystal surface and the indenter. A significant anisotropy in indentation modulus is observed with ~80 GPa difference between the highest and lowest values. Results also suggest smaller but measurable anisotropy in indentation hardness. For the single crystals with a surface normal of (1-322), (6-3-34), or (41-56), depth profiles of indentation hardness show abrupt drops in hardness upon increasing the indentation depth. Each drop in hardness is found to be associated with one pop-in event in the loading portion of indentation load vs. depth curves. The abrupt drops in hardness and pop-in events are less frequently observed for the single crystal with a surface normal of (1-21,14). Scanning electron microscopy on residual impressions of these indentations show severe cracking near the corners of the imprints, particularly at higher indentation depths. For selected indents, transmission electron microscopy (TEM) is utilized to examine the underlying deformation and failure mechanisms. Cross-sectional TEM micrographs of the indented regions show formation of a quasi-plastic zone that grows in size by increasing the indentation depth. The TEM observations also suggest planar slip is a potential carrier of quasi-plasticity and a precursor for formation of amorphous bands that could eventually lead to cracking and failure. The proposed failure mechanism provides valuable insights for calibrating constitutive computational models of failure in boron carbide.