For perspective in these photos, my field notebook is about 4 5/8" wide x 7" long.
This is a sizable egg case, probably from a Big Skate (Raja binoculata), one of the largest skates in North America. Note the size and color, the two distinctive raised dorsal ridges on the left end, and the four short, flattened horns, one at each corner. (Photos were taken on 28 February 2012.)
You may have heard this type of egg case called a "mermaid's purse". When washed up on the beach, they are often empty. But occasionally you'll find one with an egg or developing embryo inside. Big Skate egg cases are unusual in that they contain more than one egg, often between 3-7. The egg cases are attached to the sea floor (there is no parental care); juvenile skates hatch out in about 9 months.
Here's a helpful image from a research article (see citation below). The two prominent eye-like spots (one on each pectoral fin) are the reason for the species name, binoculata.
Image from Hitz, C.R. 1964. Observations on Egg Cases of the Big Skate (Raja binoculata Girard) Found in Oregon Coastal Waters. J. Fish. Res. Bd. Canada 21(4): 851-854.
Fun fact: From the inside, sometimes a developing skate will insert its tail into one of the horns at the four corners of the case to increase water flow through the egg case!
For photos and more information about Big Skates, see a species description here.