The conformation of a linear gradient copolymer chain in a homopolymer melt is investigated using theory and numerical solutions of self-consistent field equations. In the limit of large comonomer immiscibility and chain length, it is found that the copolymer collapses into a globule with monomers self-assembled into a "ball-of-yarn" conformation. The spatial heterogeneity of monomers within the globule is in striking contrast to the "tadpole" conformation of a collapsed symmetric diblock copolymer and the disordered globular state of a collapsed homopolymer or random copolymer. By simple free energy calculations, we find that the same thermodynamic factors which drive a melt of linear gradient copolymers to self-assemble into lamellar microphases in the strong-segregation regime act to drive a single copolymer to self-assemble its own monomers into the yarn ball conformation when in a homopolymer melt with which it is immiscible. Moreover, by considering self-assembly of monomers within the globule of a collapsed copolymer, we find that the thermodynamic stability of a linear gradient is less than a symmetric diblock a conclusion that is not possible to obtain by assuming that the copolymers pack their monomers randomly upon collapse.