The abundance patterns observed in the Sun and in metal-poor stars show a clear odd-even effect. An important question is whether the odd-even effect in solar-metallicity stars is similar to the Sun, or if there are variations that can tell us about different chemical enrichment histories. In this work, we report for the first time observational evidence of a differential odd-even effect in the solar twin HIP 11915, relative to the solar odd-even abundance pattern. The spectra of this star were obtained with high resolving power (140 000) and signal-to-noise ratio ($sim$420) using the ESPRESSO spectrograph and the VLT telescope. Thanks to the high spectral quality, we obtained extremely precise stellar parameters ($sigma(T_{rm eff})$ = 2 K, $sigma(rm{[Fe/H]})$ = 0.003 dex, and $sigma(log g)$ = 0.008 dex). We determine the chemical abundance of 20 elements ($Zleq39$) with high precision ($sim$0.01 dex), which shows a strong pattern of the odd-even effect even after performing Galactic Chemical Evolution corrections. The odd-even effect is reasonably well-reproduced by a core-collapse supernova of 13 $rm{M_{odot}}$ and metallicity Z = 0.001 diluted into a metal-poor gas of 1 $rm{M_{odot}}$. Our results indicate that HIP 11915 has an odd-even effect slightly different than the Sun, thus confirming a different supernova enrichment history.