Pour boiling water over your chai tea bag in a mug or small saucepan and let it steep for about 4 to 5 minutes. The longer you let it sit, the bolder and spicier the chai flavor becomes. Once it's steeped, remove the tea bag and set the tea aside.
While your tea steeps, go ahead and brew your espresso shot using whatever machine or method you have on hand. If you don't own an espresso machine, a moka pot or strongly brewed coffee works as a solid substitute. Pour the hot espresso directly into your steeped chai to combine the flavors right away.
Heat your milk in a small saucepan or with a steamer until it's hot but not boiling, around 150°F if you're using a thermometer. Use a handheld frother, whisk, or French press to whip air into the milk until it turns light and foamy. This step is what gives your latte that classic coffee shop texture.
Pour your frothed milk over the chai and espresso mixture, spooning a little extra foam on top if you have it. Stir in your sugar or honey now if you want a sweeter drink, adjusting the amount based on your taste. Give everything a gentle stir so the flavors blend evenly.
Finish your dirty chai latte with a light dusting of ground cinnamon or a sprinkle of leftover chai spice on top. Serve it immediately while it's still warm and the foam is fresh. If you prefer it cold, pour the whole mixture over a glass of ice instead.