CREATE TABLE chicken(chickenID INT PRIMARY KEY, eggID INT);
CREATE TABLE egg(eggID INT PRIMARY KEY, chickenID INT);

Then, we add foreign key constraints:

ALTER TABLE chicken ADD CONSTRAINT chicken_gg
    FOREIGN KEY (eggID) REFERENCES egg(eggID)
    INITIALLY DEFERRED DEFERRABLE;
ALTER TABLE egg ADD CONSTRAINT egg_chicken
    FOREIGN KEY (chickenID) REFERENCES chicken(chickenID)
    INITIALLY DEFERRED DEFERRABLE;