Get the unique constraint columns list (in TSQL)?

Ed is correct, the columns are exposed on the constraint column usage view, here is the SQL for it.

select TC.Constraint_Name, CC.Column_Name from information_schema.table_constraints TC
inner join information_schema.constraint_column_usage CC on TC.Constraint_Name = CC.Constraint_Name
where TC.constraint_type = 'Unique'
order by TC.Constraint_Name

SELECT *
FROM    sys.indexes i
        JOIN sys.index_columns ic
            ON i.index_id = ic.index_id
               AND i.object_id = ic.object_id
WHERE i.is_unique_constraint = 1;

See INFORMATION_SCHEMA.CONSTRAINT_COLUMN_USAGE