A feature of severe COVID-19 is the onset of an acute and intense systemic inflammatory response referred to as the "cytokine storm". The cytokine storm is characterized by high serum levels of inflammatory cytokines and the subsequent transport of inflammatory cells to damaging levels in vital organs (e.g., myocarditis). Immune trafficking and its effect on underlying tissues (e.g., myocardium) are challenging to observe at a high spatial and temporal resolution in mouse models. In this study, we created a vascularized organ-on-a-chip system to mimic cytokine storm-like conditions and tested the effectiveness of a novel multivalent selectin-targeting carbohydrate conjugate (composed of DS - dermatan sulfate and IkL - a selectin-binding peptide, termed DS-IkL) in blocking infiltration of polymorphonuclear leukocytes (PMN). Our data shows that cytokine storm-like conditions induce endothelial cells to produce additional inflammatory cytokines and facilitate infiltration of PMNs into tissue. Treatment of tissues with DS-IkL (60 μM) reduced PMN accumulation in the tissue by >50%. We then created cytokine storm-like conditions in a vascularized cardiac tissue-chip and found that PMN infiltration increases the spontaneous beating rate of the cardiac tissue, and this effect is eliminated by treatment with DS-IkL (60 μM). In summary, we demonstrate the utility of an organ-on-a-chip platform to mimic COVID-19 related cytokine storm and that blocking leukocyte infiltration with DS-IkL could be a viable strategy to mitigate associated cardiac complications.