We report growth of one-dimensional semiconductor nanocrystals, nanowhiskers, in which segments of the whisker with different composition are formed, illustrated by InAs whiskers containing segments of InP. Our conditions for growth allow the formation of abrupt interfaces and heterostructure barriers of thickness from a few monolayers to 100s of nanometers, thus creating a one-dimensional landscape along which the electrons move. The crystalline perfection, the quality of the interfaces, and the variation in the lattice constant are demonstrated by high-resolution transmission electron microscopy, and the conduction band off-set of 0.6 eV is deduced from the current due to thermal excitation of electrons over an InP barrier.