How do I prevent smoked brisket from being chewy?
Chewy means undercooked. Most of your standard "barbecue cuts" of meat contain a lot of connective tissue. This must be rendered to achieve tenderness. This goes for brisket, pork butt, and ribs, to name a few. If you are using the words "chewy" or "tough" to describe the texture of your meat, in nearly all cases it has not been cooked enough. Your time/temperature pretty much confirms it.

The best thing you can do is deemphasize time and temperature as your measure of "done." Rather, use a skewer to probe your meat when you think you are getting close. It should slide in and out of the brisket with VERY little resistance. Some people like to wrap in foil a few hours in. This will finish the brisket faster, as you will mitigate the evaporative cooling effect that causes your cooking process to stall. Plus, you can add some liquids and spices to the foil, which adds to the flavor profile of your meat. This is better known as the "Texas Crutch," and there is no shame in using it. Plenty of competitions have been won employing these tactics.

Brisket is a little intimidating because of the small window between "too chewy" and "dry and falling apart." But you should probably err more on the side of the latter, as that can be more easily compensated. The real takeaway here is have patience, and look to the meat itself for clues as to whether or not it is done, rather than using a timer and thermometer.