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I am sorry to hear you are worried about your Chihuahua. I am a veterinarian, and will do my best to help.
How much do you think he drank? 1 teaspoon, more? If he got a small amount it will not harm him; these beverages are mostly sugar and milk, but if he got enough caffeine, he could have tremors or develop a high heart rate. I would have to know the brand, and how much he drank, to estimate the amount of caffeine he got.
If this just happened, you could try to induce vomiting with a 1/2 teaspoon of hydrogen peroxide in milk. That should empty his stomach, but only if he got this in the last few minutes.