yes this branch is dead so cut it back to healthy growth.

You would have nothing to lose by cutting off the branch. Just bare in mind as you say that it is a large Ceanothus which I guess is quite old but they don't seem to be particularly long livers so perhaps its had its day; although some members will have subjects that are quite aged.

We inherited one here which must be over 20 years old and it doesn't seem to mind at all when I cut a dead branch off it. That's a pretty big one but the looks of it but you've got nothing to lose. Try it.

Thanks to you all. Yes, it's at least 7 years old and over 10 foot tall. It used to flower all over up until the last year or so.

Might well rejuvenate it to give it a hard chop!

Ceanothus are relatively short lived, making about 10-20 years at most, though occasionally, some survive for a bit longer than that. Agree with everyone else, remove the dead branch, but you may find its on its way out as its over 20 years old.