Chat gpt 4 plus chat history?

Can gpt-4 Plus using GPT-4 remember everything we talked about earlier in the conversation from the same chat?

Short answer: No.
ChatGPT (and API calls) have what’s called a “context window” that’s limited to a certain threshold of tokens. Tokens are what ChatGPT uses instead of counting “words” or other lexical information.
Now, according to OpenAI dev day, ChatGPT 4 in ChatGPT plus should now have (or will have soon) a context window of over 100,000 tokens iirc. Simply put; that’s a lot of data. For comparison, it’s about the size of an average novel. Whether or not you exceeded that limit depends on the data you feed into it, but chances are (unless you’re doing frequent, dense, advanced data analysis) you likely won’t hit that limit for a while.