Using muon spin resonance we examine the organometallic hybrid compound Cu(1,3-benzenedicarboxylate) [Cu(1,3-bdc)], which has structurally perfect spin 1/2 copper kagome planes separated by pure organic linkers. This compound has antiferromagnetic interactions with Curie-Weiss temperature of -33 K. We found slowing down of spin fluctuations starting at T=1.8 K, and that the state at T->0 is quasi-static with no long-range order and extremely slow spin fluctuations at a rate of 3.6 1/usec. This indicates that Cu(1,3-bdc) behaves as expected from a kagome magnet and could serve as a model kagome compound.