The quantum walk is the quantum analogue of the well known random walk and has been proposed for numerous applications in quantum information science. Coherent superposition and matter wave interference lead to markedly different properties of the quantum walk compared to its classical counterpart. I will report on the experimental realization of a quantum walk using single neutral atoms trapped in a state-dependent optical lattice. Site-resolved fluorescence imaging in the lattice allows us to probe and characterize the delocalized wave function of an atom with local quantum state tomography. This allows us to investigate the characteristic features of the quantum walk and to observe the gradual quantum-to-classical transition as the particle is performing an increasing number of steps.