We present the experimental synthesis of one-dimensional (1D) van der Waals heterostructures, a class of materials where different atomic layers are coaxially stacked. We demonstrate the growth of single-crystal layers of hexagonal boron nitride (BN) and molybdenum disulfide (MoS2) crystals on single-walled carbon nanotubes (SWCNTs). For the latter, larger-diameter nanotubes that overcome strain effect were more readily synthesized. We also report a 5-nanometer-diameter heterostructure consisting of an inner SWCNT, a middle three-layer BN nanotube, and an outer MoS2 nanotube. Electron diffraction verifies that all shells in the heterostructures are single crystals. This work suggests that all of the materials in the current 2D library could be rolled into their 1D counterparts and a plethora of function-designable 1D heterostructures could be realized.