Diffuse insterstellar bands (DIBs) are absorption features in the spectra of reddened stars, caused by the absorption of light by the interstellar medium. Organic molecules based on polycyclic aromatic hydrocarbons (PAHs), revealed by infrared emission bands, are present in the interstellar medium and are considered to be possibly responsible for DIBs. However, the specific carbon-based nanostructures are still unidentified, with the notable exception of C60+ (Campbell et al. 2015, Nature, 523, 322). In the present work, using state-of-the-art time-dependent density functional theory (TDDFT) and many-body perturbation theory within the GW approximation, we predict that carbon chains (carbynes) connected to PAH groups exhibit absorption spectra that can be tuned in the energy window of the unexplained DIB spectrum. Our theoretical results reveal electronic transitions in both the visible and near-infrared range depending on the length of the carbyne chain and the nature of the connected PAHs, thus providing new insights into the possible carbon-based species populating interstellar space.