VATICAN CITY—A chain of Catholic psychiatric hospitals in Belgium is granting euthanasia to non-terminal patients, defying the Vatican and deepening a challenge to the church’s commitment to a constant moral code.

The board of the Brothers of Charity, Belgium’s largest single provider of psychiatric care, said the decision no longer belongs to Rome. Truly Christian values, the board argued in September, should privilege a “person’s choice of conscience” over a “strict ethic of rules.”