Here is a simple implementation of the Twitch.tv chatbot using the GPT-3 API:

```python
import openai

# Initialize API key for OpenAI
openai.api_key = "YOUR_API_KEY"

# Define the chatbot's name
BOT_NAME = "ChatGPT"

# Retain a history of comments in a list
chat_history = []

# Continuously listen to the chat stream and respond when addressed directly by name
while True:
    # Get the latest comment in the chat
    comment = get_latest_comment()

    # Add the comment to the chat history
    chat_history.append(comment)

    # Check if the comment mentions the chatbot's name
    if BOT_NAME in comment:
        # Use GPT-3 to generate a response
        response = openai.Completion.create(
            engine="text-davinci-002",
            prompt=f"{BOT_NAME}, {comment}",
            max_tokens=1024,
            n=1,
            stop=None,
            temperature=0.5,
        ).choices[0].text

        # Post the response in the chat
        post_message(response)


```

Note: The code assumes the existence of two functions, `get_latest_comment()` and `post_message(message)`, which are responsible for fetching the latest comment from the Twitch chat and posting a message to the Twitch chat, respectively. You will need to implement these functions based on the specific Twitch API you are using.
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