Mass-independent isotopic anomalies in meteorites are probes to the dynamics and evolution of the protoplanetary disc and the reservoirs from which planetary bodies accreted. Variable Cr nucleosynthetic compositions between meteorite groups are observed but the cause is not well understood. Investigations on presolar carriers in unequilibrated chondrites are thus required to establish these relationships. For that purpose, we analysed the Cr isotope compositions of leachates (stepwise dissolution solutions) of one ordinary chondrite and two enstatite chondrites of EL and EH subgroups previously measured for Nd and Sm isotopes. The leachates of the ordinary chondrite display large variations of their Cr isotope compositions, whereas the leachates of the enstatite chondrites show very limited variations of their nucleosynthetic compositions, confirming other studies. The Cr isotope compositions of leachates of unequilibrated chondrites are significantly modified by thermal processing and aqueous alteration under various conditions. The leachates of the enstatite chondrites are relatively homogeneous for Cr isotope composition, suggesting that presolar carriers of Cr are not stable under very reduced conditions and are likely oxidised phases. After careful examination of the role of parent body processing, we conclude that there is one predominant presolar carrier enriched in 54Cr that produced most of the nucleosynthetic variations observed in leachates. This carrier is likely depleted in the carbonaceous reservoir relative to the non-carbonaceous reservoir. The drastically different isotope compositions of Cr and heavy refractory lithophile elements such as Nd of leachates of chondrites reflect relative preservation biases of their respective presolar carriers, namely a still poorly characterised presolar oxide and silicon carbide (SiC), respectively.