We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor SO(N) singlet projectors on the kagome lattice. Our model shares some features with the popular S = 1/2 kagome antiferromagnet but is specifically designed to be free of the sign problem of quantum Monte Carlo. In our numerical analysis, we find as a function of N a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-N generalization suggests that the quantum spin liquid in our original model is a gapped Z(2) topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.