While the company looks for a replacement, its finance team will report to Jacques Tortoroli, the controller for parent company Viacom.
The decision to leave was Chestnut's, according to a company spokesperson.
Chestnut was charged with managing MTVN's financial operations and served on the MTVN Management Committee, which oversees major issues in the company's management.
She joined MTVN from the JWT ad agency, where she served as North American CFO since 2000. Before that, she was The Americas CFO of TBWA Worldwide from 1995-2000.