|From the point of view of elementary particle physics the gravitational constant G is extraordinarily small. This has led to ask whether it could have decayed to its present value from an initial one commensurate with microscopical units. A mechanism that leads to such a decay is proposed herein. It is based on assuming that G may take different values within regions of the universe separated by a novel kind of domain wall, a “G-wall”. The idea is implemented by introducing a gauge potential A, and its conjugate D, which determines the value of G as an integration constant rather than a fundamental constant. The value of G jumps when one goes through a G-wall. The procedure extends one previously developed for the cosmological constant, but the generalization is far from straightforward: (i) The intrinsic geometry of a G-wall is not the same as seen from its two sides, because the second law of black hole thermodynamics mandates that the jump in G must cause a discontinuity in the scale of length. (ii) The size of the decay step in G is controlled by a function G(D) which may be chosen so as to diminish the value of G towards the asymptote G = 0, without fine tuning. It is shown that: (i) The dynamics of the gravitational field with G treated as a dynamical variable, coupled to G-walls and matter, follows from an action principle, which is given. (ii) A particle that impinges on a G-wall may be refracted or reflected. (iii) The various forces between two particles change when a G-wall is inserted in between them. (iv) G-walls may be nucleated trough tunneling and thermal effects. The semiclassical probabilities are evaluated. (v) If the action principle is constructed properly, the entropy of a black hole increases when the value of the gravitational constant is changed through the absorption of a G-wall by the hole.