Qualitative insight into the properties of a quantum-mechanical system can be gained from the study of the relationship between the system’s classical newtonian dynamics, and its quantum dynamics as described by the Schrodinger equation. The Bohr-Sommerfeld quantization scheme--which underlies the historically important Bohr model for hydrogen-like atoms--describes the relationship between the classical and quantum-mechanical regimes, but only for systems with stable, periodic or quasiperiodic orbits’. Only recently has progress been made in understanding the quantization of systems that exhibit non-periodic, chaotic motion. The spectra of quantized energy levels for such systems are irregular, and show fluctuations associated with unstable periodic orbits of the corresponding classical system(1-3). These orbits appear as ’scars’-concentrations of probability amplitude--in the wavefunction of the system(4). Although wavefunction scarring has been the subject of extensive theoretical investigation(5-10), it has not hitherto been observed experimentally in a quantum system. Here we use tunnel-current spectroscopy to map the quantum-mechanical energy levels of an electron confined in a semiconductor quantum well in a high magnetic held(10-13). We find clear experimental evidence for wavefunction scarring, in full agreement with theoretical predictions(10).