Step 1: Recall Indian coffee production geography.
Coffee is primarily grown in the hilly regions of southern India, where the climate is cool, the soil is well-drained, and rainfall is adequate.
Step 2: Identify the leading state.
Karnataka is the largest coffee-producing state in India, contributing about 70-75% of the country's total coffee output. The Coorg (Kodagu), Chikmagalur, and Hassan districts are famous coffee-growing regions.
Step 3: Eliminate other options.
Kerala and Assam produce tea predominantly; Chhattisgarh has negligible coffee production.
\[ \boxed{\text{Karnataka}} \]