The potential complementarity between chondrules and matrix of chondrites, the Solar System's building blocks, is still a highly debated subject. Complementary superchrondritic compositions of chondrite matrices and subchondritic chondrules may point to formation of these components within the same reservoir or, alternatively, to mobilization of elements during secondary alteration on chondrite parent bodies. Zinc isotope fractionation through evaporation during chondrule formation may play an important role in identifying complementary relationships between chondrules and matrix and is additionally a mobile element during hydrothermal processes. In an effort to distinguish between primary Zn isotope fractionation during chondrule formation and secondary alteration, we here report the Zn isotope data of five chondrule cores, five corresponding igneous rims and two matrices of the relatively unaltered Leoville CV3.1 chondrite. The detail required for these analyses necessitated the development of an adjusted Zn isotope analyses protocol outlined in this study. This method allows for the measurement of 5 ng Zn fractions, for which we have analyzed the isotope composition with an external reproducibility of 120 ppm. We demonstrate that we measure primary Zn isotope signatures within the sampled fractions of Leoville, which show negative δ66 Zn values for the chondrule cores (δ66 Zn=-0.43±0.14‰), more positive values for the igneous rims (δ66 Zn=-0.01±0.30‰) and chondritic values for the matrix (δ66 Zn=0.19±0.14‰). In combination with elemental compositions and petrology of these chondrite fractions, we argue that chondrule cores, igneous rims and matrix could have formed within the same reservoir in the protoplanetary disk. The required formation mechanism involves Zn isotope fractionation through sulfide loss during chondrule core formation and concurrent thermal processing of matrix material. Depleted olivine-bearing grains representing this processed matrix would have accreted to the depleted chondrule cores and subsequently reabsorbed material (including 66 Zn-rich) from a complementary volatile-rich gas, thereby forming the igneous rims. This would have allowed the rims to move towards an isotopically chondritic composition, similar to the non-processed matrix in Leoville. We note that Zn isotope analyses of components in other chondrites (f.e., CM, CO, EC) are necessary to identify if this complementarity relationship is generic or unique for each chondrite group. The development of a Zn isotope protocol for singularly small samples is a step forward in that direction.