We introduce and study a compromise value for non-transferable utility games: the Chi-compromise value. It is closely related to the Compromise value introduced by Borm, Keiding, McLean, Oortwijn, and Tijs (1992) and to the MC-value introduced by Otten, Borm, Peleg, and Tijs (1998). The main difference being that the maximal aspiration a player may have in the game is his maximal (among all coalitions) marginal contribution. We show that it is well defined on the class of essential and non-level games.Financial support from the Spanish Ministry of Education and Culture through grants PB98-0870 and PB98-0613-C02-01 and from the Comissionat per Universitats i Recerca de la Generalitat de Catalunya through grant SRG98-0062 is gratefully acknowledged.