After posting the question in the Chromebooks Google+ Community which describes itself as the "largest unofficial community for Chrome OS discussion," I received an overwhelming nudge in the direction of +LastPass in lieu of +1Password.
(As a side note, I would highly recommend this community as it has a very active and engaged user base. I have found it very helpful to connect with other "Chromies" who are trying to figure out how to harness the power—yes I said power—of this emerging technology platform.)
- You get a first-class password tool. Unless you are in a hyper-sensitive industry, the power of LastPass security features will overwhelm you at first. Take a breath and let it make you feel comfortable that you are using a robust tool.
- LastPass is tied to your browser and your vault in the Cloud. It isn't housed locally on your hard drive and isn't shared over a file-sharing service like Dropbox.
- I can share passwords with people on my team without revealing the actual password. This makes password management for my assistant and my project coordinator that much easier.
- LastPass allows me to store just about anything. It's not just for passwords. You can also store notes to credit card information.
- LastPass scores my passwords and tells me where I am weak. It is simple to update those passwords. Those updates are immediately available on every device I have that is also logged into LastPass.
- If you need it, you can add things like a +YubiKey and two-step verification for Google. I haven't taken this step yet, but it's a nice option.
- The customer support is fantastic. I had a quick follow up email from a real person soon after subscribing. When I asked a question, they actually responded. I was impressed.