We introduce a model of coagulation with single-particle breakoft', described by the kernels K~1 ij and F1 a((j+1)b;& +(i+1)bj&). For a above a critical value a„the system either gels or reaches a steady-state size distribution, depending upon initial conditions. Below a„gelation always occurs. At a a„the scaling exponent i, which describes the large-size behavior of the steady-state size distribution, is 2 rather than the usual value &, indicating that this process belongs to a new universality class of gelation.