Complex sentence: Chenier's popularity peaked in the 1980s, when he won a Grammy Award in 1983 for his album "I'm Here", the first Grammy for his new label Alligator Records.
Split into simpler sentences: Chenier's popularity peaked in the 1980s, and he was recognized with a Grammy Award in 1983 for his album "I'm Here". It was the first Grammy for his new label Alligator Records.