We report the design and synthesis of the acyclic cucurbit[n]uril-β-cyclodextrin chimeric host H1. The goal of the study is to deepen the cavity of the receptor to allow β-CD complexation of moieties on the guest (especially fentanyl) that protrude from the cavity of the primary acyclic CB[n] binding site to enhance binding affinity and deliver new supramolecular antidotes for fentanyl intoxication. 1H NMR spectroscopy was used to deduce the geometry of the complexes between H1 and H2 and the guest panel (G1 - G8 and fentanyl) whereas isothermal titration calorimetry was used to determine the thermodynamic parameters of complexation. Hosts H1 and H2 retain the essential molecular recognition features of CB[n] receptors, but chimeric host H1 binds slightly stronger toward the guest panel than H2 for reasons that remain unclear. Compared to tetraanionic hosts M1 and M2, the dianionic hosts H1 and H2 are less potent receptors which reflects the importance of electrostatic (ion-ion and ion-dipole) interactions in this series of hosts. The work highlights the challenges inherent in the optimization of binding affinity of hosts as potential supramolecular antidotes.