I had wondered about a bivalve periostracum (the outermost layer)...and also about a snail's operculum (the "trap door"), as had a few other folks. But I wasn't satisfied with either possibility.
For example, after checking various books, I couldn't find any clam with this shape. And, although I started looking at snail opercula, and some of them were closer in shape, the material (very thin and flexible), the chalky layer, and an odd twist along one side of the shell, didn't match with any operculum I was familiar with. Here's a picture of the twist that puzzled me:
However, a breakthrough came today via a Twitter exchange! Annaliese (at Oregon State University) sent out a request for assistance and Rebecca (at the California Academy of Sciences) responded with an identification, including a photo!
Here's the photo of a dried specimen from the California Academy of Sciences:
Compare that with my mystery specimen from Dillon Beach (now dried out, see below):
You can see how similar the shape and texture are.
I agree with Rebecca that this is a good match with her sample which is the *internal* shell of a California Sea Hare (Aplysia californica)! I'll admit that I hadn't known (or had forgotten) that Aplysia had an internal shell, and I've certainly never seen hide nor hare of such a shell. ;)
I know that this phenomenon might be confusing at first, but there are some snail relatives (like sea hares) that have internal shells that aren't visible from the outside. Here's a link to a diagram showing the development of a California Sea Hare (see Research study 2). Note that they have an external shell when very young, but the shell becomes internal in the adults.
Many thanks to Rebecca and Annaliese for solving the mystery!
P.S. Adult California Sea Hares were observed in Sonoma and Marin counties in 2015 and 2016. To review what the adults look like, see the posts from 28 September 2016 and 23 May 2015.