Not likely, given that even unsweetened cocoa has a notable amount of carbs in it.

This is the closest I ever found that wasn't just something like Walden Farms syrup in water, and it's still 6g net.
http://www.ruled.me/creamy-keto-hot-cocoa/

Avalanche sugar free hot chocolate has 0.3g of carbs

Well this is timely - would you all believe that the last thing my son said to me last night was "tomorrow can you help me experiment with making low carb hot chocolate? Please?" You all seriously read his mind!

My current recipe for BPCocoa since I don't drink coffee (@Phrick - I've had to work at balance on this one, but I love it, and it tastes better than the NSA stuff I bought for work!)

8-10 oz unsweetened vanilla almond milk
3 TBSP butter (or less if using any heavy cream)
1 TBSP MCT oil (I used up my bottle today and accidentally used a bit more, I think)
1 scoop collagen powder
1-2 TBSP raw cacao powder
1 "dash" vanilla powder (will be switching to alcohol free vanilla when this is gone - has sugar in it/didn't know)
2 droppers SweetLeaf Stevia
2-4 oz hot water

Optional: splash heavy cream, dash salt

Since I make this at work, I microwave the butter and almond milk. While that's warming, I add everything else to my "mixing mug" and blend together with my frother. Once the butter/almond milk is heated, I add about half of it, blend, then the rest, and blend again. I add hot water to taste... Added the recipe to MFP. 10 grams carbs, 5 net grams carbs, but this is my breakfast MEAL... I didn't measure the cacao powder exactly, so I rounded up, and it would be just a little higher on carbs if I used heavy cream (I should add 1-2 carbs for the current vanilla powder I use even though MFP doesn't count it, as I know there's some sweetener in it). Now this is higher in carbs @sas1uk - but this recipe, I control everything that goes in it, the ingredients are all of great quality, I don't have AS I don't like or weird fillers, and I'm quite happy to have this every day, adjusting a little up or down. It works for me without having any crashes afterward, and yes, the majority of the carbs from the cacao powder, which is awesome and way taster than traditional grocery store cocoa powder!

Nutrition Facts
Servings 1.0
Amount Per Serving
calories 604
% Daily Value *
Total Fat 68 g 104 %
Saturated Fat 52 g 260 %
Monounsaturated Fat 2 g
Polyunsaturated Fat 1 g
Trans Fat 0 g
Cholesterol 90 mg 30 %
Sodium 230 mg 10 %
Potassium 284 mg 8 %
Total Carbohydrate 10 g 3 %
Dietary Fiber 5 g 19 %
Sugars 0 g
Protein 11 g 22 %
Vitamin A 37 %
Vitamin C 0 %
Calcium 58 %
Iron 11 %
* The Percent Daily Values are based on a 2,000 calorie diet, so your values may change depending on your calorie needs. The values here may not be 100% accurate because the recipes have not been professionally evaluated nor have they been evaluated by the U.S. FDA.

Aztec style also has chili (capsicum for you UK'ers). Very tasty and a real peppy morning drink.