Currently, there isn't a convenient way to access Google Tasks from a desktop computer. While Google services like Calendar and Keep have their own fully featured web apps, Google Tasks is squirreled away behind a side panel menu inside those other services. You've long been able to work around this on ChromeOS by using the Tasks Android app, but now, it seems Google's working on integrating your Tasks right into ChromeOS's system tray.
About Chromebooks reports that code relating to native Tasks integration in ChromeOS has cropped up in the Chromium Gerrit. Aside from that the project is in progress, there's not really much information to go on just yet, but it seems like Google Tasks will live in the system tray in the lower right corner of the screen, working in a similar way to the Google Calendar integration Chromebooks picked up in ChromeOS 99 last year. Think an icon that, when clicked, opens a floating to-do list populated with Google Tasks.
It's not clear when we can expect to see this functionality in preview builds, but development seems to be in the early stages. About Chromebooks says that, with the code in its current state, it wouldn't be possible to check off sub-tasks nested under primary tasks, which would make organizing larger projects using this new tool a major hassle.
It's been an eventful few days in the ChromeOS space. Earlier this week, we reported that the latest developer build of ChromeOS comes with new dynamic screensavers — so even if this new Tasks integration takes time to bear fruit, Chromebook die-hards have plenty to look forward to.