Atomically-thin materials such as single-walled carbon nanotubes and graphene are prone to chemical attack because all of the constituent atoms are exposed. Here we describe the synthetic creation of a tube-in-a-tube (Tube^2) semiconductor and their implications on biochemical sensing. A Tube^2 is equivalent to a pristine single-walled carbon nanotube (SWCNT) nested within a chemically tailored, impermeable, and atomically-thick functional shell. Compared with SWCNTs and graphene, electrical sensors created using Tube^2 can be readily tailored with robust covalent chemistries to enable chemical selectivity while maintaining exceptional SWCNT-like sensitivity. Recent progress from our lab as well as some of the critical challenges and opportunities in this area will be discussed.