We describe a molecular-beam infrared-microwave-microwave triple-resonance spectroscopy technique for measuring the rotational spectrum of single quantum states in energy regions where isomerization occurs. Infrared-microwave (IR-MW) saturation spectroscopy, with a resolution of 300 KHz, has been employed for the excitation of single eigenstates. In a second step, the rotational spectrum of the prepared quantum state is measured using a technique based on the Autler-Townes splitting of states. The technique is illustrated by measurements of the rotational spectrum of single quantum stales of 4-chlorobut-1-yne near 3330 cm(-1).