The following sentence is copied from theverge.com:
"Tesla is reportedly working on a chip to handle all the tasks needed to power the fleet of fully self-driving cars that its CEO Elon Musk promised would be road-ready by 2019. "
I have no much idea about the subject and the verb in this sentence. It seems that there are two verbs dominate this sentence. Specially, "that its CEO Elon Musk promised would be road-ready by 2019".
In this clause, what is subject of would?