  We produce a trimerized kagome lattice for ultracold atoms using an optical
superlattice formed by overlaying triangular lattices generated with two colors
of light at a 2:1 wavelength ratio. Adjusting the depth of each lattice tunes
the strong intra-trimer (J) and weak inter-trimer (J') tunneling energies, and
also the on-site interaction energy U. Two different trimerization patterns are
distinguished using matter-wave diffraction. We characterize the coherence of a
strongly interacting Bose gas in this lattice, observing persistent
nearest-neighbor spatial coherence in the large U/J' limit, and that such
coherence displays asymmetry between the strongly and the weakly coupled bonds.
