With space constraints onshore, strong renewable resources available far offshore and growing green hydrogen demand, far offshore green hydrogen production may be an attractive option. To assess this potential, a mixed integer quadratically constraint programming (MIQCP) optimization model was developed to find the cost per kilogram of far offshore green hydrogen in specific scenarios. The design of the far offshore green hydrogen supply chain was optimized with this model for six high potential scenarios in varying locations and the results were analyzed. It was found that far offshore green hydrogen costs are in the same order of magnitude as the costs of its alternatives. Far offshore green hydrogen may be considered marginally competitive with these alternatives from 2035 onwards in the analyzed scenarios when taking into account the considerable advantages of far offshore production, such as avoidance of scarce land usage in crowded areas and certain geopolitical considerations.