We show that the capacitance of single-walled carbon nanotubes (SWNTs) is highly sensitive to a broad class of chemical vapors and that this transduction mechanism can form the basis for a fast, low-power sorption-based chemical sensor. In the presence of a dilute chemical vapor, molecular adsorbates are polarized by the fringing electric fields radiating from the surface of a SWNT electrode, which causes an increase in its capacitance. We use this effect to construct a high-performance chemical sensor by thinly coating the SWNTs with chemoselective materials that provide a large, class-specific gain to the capacitance response. Such SWNT chemicapacitors are fast, highly sensitive, and completely reversible.