The hollow inner spaces of single-wall carbon nanotubes (SWCNTs) can confine various types of molecules. Many remarkable phenomena have been observed inside SWCNTs while encapsulating organic molecules (peapods). However, a mixed electronic structure state of the surrounding SWCNTs has impeded a detailed understanding of the physical/chemical properties of peapods and their device applications. We present a single-chirality purification method for SWCNTs that can encapsulate organic molecules. A single-chiral state of (11,10) SWCNTs with a diameter of 1.44 nm, which is large enough for molecular encapsulation, was obtained after a two-step purification method: metal-semiconductor sorting and cesium-chloride sorting. The encapsulation of C-60 to the (11,10) SWCNTs was also succeeded, promising a route toward single-chirality peapod devices.