Using resistivity, heat-capacity, thermal-expansion, and susceptibility measurements we study the normal-state behavior of KFe2As2. Both the Sommerfeld coefficient (γ≈103 mJ mol(-1) K(-2)) and the Pauli susceptibility (χ≈4×10(-4)) are strongly enhanced, which confirm the existence of heavy quasiparticles inferred from previous de Haas-van Alphen and angle-resolved photoemission spectroscopy experiments. We discuss this large enhancement using a Gutzwiller slave-boson mean-field calculation, which shows the proximity of KFe2As2 to an orbital-selective Mott transition. The temperature dependence of the magnetic susceptibility and the thermal expansion provide strong experimental evidence for the existence of a coherence-incoherence crossover, similar to what is found in heavy fermion and ruthenate compounds, due to Hund's coupling between orbitals.