A smooth projective complex variety X is said to be Fano if its anticanonical divisor -K_X is ample. A result of Shokurov shows that if the dimension of X is equal to three, then the linear system |-K_X| is non-empty and every general element D inside |-K_X| is smooth. In dimension four we are able to construct varieties for which all such D are singular, however we determine that these singularities are at most terminal. We show that the Kawamata Nonvanishing Conjecture implies the same result in arbitrary dimension.