West Sussex Fire and Rescue Service said crews were called shortly after 1.30pm to a 'well-alight' van on Whiteways Lodge roundabout, near Madehurst.
A spokesperson said crews were still in attendance as of 2.40pm.
It added: "Two fire trucks from Littlehampton are on the scene. Police have shut the road."
In a post on social media, Chichester Police said officers put down a cordon to 'protect the public'.
It added: "Our Prevention Officers on route from Horsham were the first responders to this incident at the junction of A29 and Madehurst. We are pleased to report that all occupants of the van are safe and well.
"West Sussex Fire and Rescue are now on scene and the fire is nearly out. Please avoid this junction for the time being and find an alternative route."