We point out that an anomalous gauge U(1) symmetry is a natural candidate for being the mediator and messenger of supersymmetry breaking. It facilitates dynamical supersymmetry breaking even in the flat limit. Soft masses are induced by both gravity and the U(1) gauge interactions giving an unusual mass hierarchy in the sparticle spectrum which suppresses flavor violations. This scenario does not suffer from the Polonyi problem. [S0031-9007(96) PACS numbers: 12.60. Jv, 04.65. + e, 11.30.Na, 14.80.Ly The origin of supersymmetry breaking remains an open question. More important, for phenomenological purposes, it is to know how the breaking of supersymmetry is transmitted to the ordinary particles. The most popular scenario arises in the context of supergravity. In these theories supersymmetry is assumed to be broken in some isolated hidden sector and transmitted to the observable sector by gravity [1]. These models, however, suffer from certain drawbacks. The degeneracy of the scalar quarks needed to avoid large flavor changing neutral currents (FCNC) is not usually guaranteed at low energies. Also the breaking of supersymmetry results in the nonflat limit leading to cosmological disasters (the Polonyi problem [2]).In this Letter we will consider an alternative scenario. It is well known that extra U(1) factors normally appear in effective field theories arising from strings. One of these U(1) is usually anomalous. The cancellation of its anomalies occurs by the Green-Schwarz mechanism [3] and requires that both hidden and observable fields transform nontrivially under this U(1). Thus this anomalous U(1) seems to be a natural new candidate for transmitting the supersymmetry breaking from the hidden to the observable sector. Here we will study this possibility.Since the U(1) is anomalous, Tr Q fi 0, a FayetIliopoulos term of O ͑M 2 P ͒ is always generated [4]. This term facilitates the breaking of supersymmetry in the flat limit, avoiding the Polonyi problem. The scale of supersymmetry breaking can be smaller than M P and can originate dynamically. In the presence of gravity, realistic scalar and gaugino masses are induced in the observable sector. We find that the D-term contribution can be larger than the gravity mediated F-term contribution, resulting in a hierarchy of soft masses. This is a crucial difference with the conventional hidden sector scenarios in supergravity models. As we will show, our model can lead to a certain degree of squark degeneracy and suppressed FCNC. It also allows for an explanation of the observed quark mass hierarchy (m t,b ¿ m u,d , m c,s ) and predicts an inverse hierarchy for the squarks (m