The aircraft, operated by the Airborne Tactical Advantage Company, went down as it was nearing Naval Base Ventura County in Oxnard, about halfway between the coastal cities of Santa Barbara and Santa Monica.
Capt. Mike Lindberry, a spokesman for the Ventura County Fire Department, tweeted it's not known whether the Hunter Hawker aircraft's pilot "ejected or if chute was part of (the) debris field."
ATAC flies small jets used in exercises at the Navy base, according to base spokeswoman Kimberly Gearhart. She said that the contractor leases space on the base.
Naval Base Ventura County was established in 2000, combining two World War II-era locales in Naval Air Station Point Mugu and Construction Battalion Center Port Hueneme. It's now home to more than 80 military commands, according to the base's website.