At the age of six, Cox began working on family farms and in family businesses. He put himself through IU by creating a mimeograph enterprise and a transportation service between Bloomington and Indianapolis. After earning a business degree from IU in 1944, he founded his own business, J.H. Cox Manufacturing.

He later purchased a bankrupt company and created Aero Drapery, which grew over several decades to become a thriving Indianapolis firm with 920 employees. He farmed nearly 1,500 acres in Boone, Hamilton and Putnam counties and managed commercial real estate and agricultural investments.

In 1999, Cox and his late wife, Beulah, donated 126 acres and three homes to the Hamilton County Parks Department to create the Coxhall Gardens in Carmel, Ind. Cox's generosity established the Jesse H. and Beulah Chanley Cox Scholars program, which provides scholarships for working students on IU's Bloomington and Indianapolis campuses, and the pavilion in the Arboretum at IU Bloomington also bears the Coxes' name. Cox was named a Sagamore of the Wabash by Indiana Gov. Frank O'Bannon in 2002. He resides in Carmel, Ind.