In this work we assessed the hypothesis that stars in wide binary systems are chemically homogeneous because of their shared origin. We obtained the abundances of the HIP 34407/HIP 34426 binary by analyzing high-resolution spectra of the system. Our results indicated a mean metallicity discrepancy of Δ[M/H] ~0.22 decimal exponent (dex) between the two components, with HIP 34426 being the poorer in [X/Fe]. We observed an overall abundance difference of Δ[X/H] ~0.18 dex. We found that HIP 34426 showed an oddly high volatile vs. refractory element ratio of ~1.72 dex when compared to its companion’s ratio of ~0.68 dex. We detected a Pearson correlation coefficient of -0.77 between the elemental condensation temperature and the differences in abundances. Lastly, we noted the presence of irregularities in the radial velocity data of HIP 34426. We speculated that this phenomenon, along with the system’s discrepancy in elemental abundances, might be an indicator of the presence of rocky planets around this star. We concluded that the differences found in chemical composition might demonstrate limitations in the assumptions of chemical tagging.