Final answer:
Timothy Leary, a Harvard professor, promoted the use of LSD and popularized the phrase 'tune in, turn on, drop out'.
Step-by-step explanation:
The Harvard professor who promoted the use of the drug LSD and coined the phrase 'tune in, turn on, drop out' is Timothy Leary. Leary was a psychologist and advocate for the use of psychedelic drugs. He believed that LSD could expand one's consciousness and lead to personal and social transformation.