Since Google sees ChatGPT as a threat of the current search paradigm (and they should), I expect they start adopting and enable a "conversational" mode similar to what Perplexity AI does with OpenAI GPT 3.5 and Microsoft Bing here soon to avoid being left behind and shift in a way that poses less risk: https://www.perplexity.ai/
Perplexity AI

Perplexity AI unlocks the power of knowledge with information discovery and sharing.

@aleyda Some guesses here:
Msft is sponsoring OpenAI. Bing can provide a (near) real-time data pipeline of search queries to OpenAI. They can use that to train the AI.
This might result in Bing integrating OpenAI WebGPT or ChatGPT in Bing's search results before even Google does something similar.

I find this article very interesting about it:
https://openai.com/blog/webgpt/

WebGPT: Improving the Factual Accuracy of Language Models through Web Browsing

We've fine-tuned GPT-3 to more accurately answer open-ended questions using a text-based web browser. Our prototype copies how humans research answers to questions online—it submits search queries, follows links, and scrolls up and down web pages. It is trained to cite its sources, which makes it easier to give

OpenAI