We report the first observations of resonant tunneling in electronic transport perpendicular to two AlAs layers separated by a GaAs quantum well in GaAs/AlAs heterostructures grown by metalorganic chemical vapor deposition. Resonant tunneling can be observed as inflections in the I-V curves at room temperature. These inflections become more pronounced as the temperature is reduced, until negative differential resistance regions become visible for temperatures below 260 K. At low temperatures, the I-V curves not only reveal two large negative resistance regions corresponding to the first energy level in the GaAs quantum well but also a structure which shows evidence of resonant tunneling through the second and possibly the third energy states in the well. Second derivative (d2I/dV2) measurements confirm the existence of the resonances seen in the I-V curves.