We examine the organometallic hybrid compound Cu(1,3-benzenedicarboxylate) [Cu(1,3-bdc)], which has structurally perfect spin 1/2 copper kagomé planes separated by pure organic linkers. This compound has antiferromagnetic interactions with Curie-Weiss temperature of -33 K. Using muon spin resonance we found slowing down of spin fluctuations starting at T=1.8 K, and that the state at Tà0 is quasi-static with no long-range order and extremely slow spin fluctuations at a rate of 3.6 µsec^-1. Susceptibility measurements along and perpendicular to the kagomé plane are used to clarify the spin Hamiltonian. Our experiments indicates that Cu(1,3-bdc) behaves as expected from a kagomé magnet with anisotropic interactions, and could serve as a model kagomé compound.