My first intuition is that it should be:
I scheduled a meeting for you and I to chat.
But then I noticed that I would use "me" in:
Patrick scheduled a meeting for you and me.
and
Patrick scheduled a meeting for me to chat with him.
I think the reason I’m struggling is that in the first sentence, I cannot tell whether "you and I" plays the role of an object (for whom the meeting is scheduled) or the subject (who is chatting).
Answer
It’s "you and me", not "you and I". You are using "to chat" as an adverbial infinitive here. Think of how it sounds by replacing "you and me" with "us" versus "you and I" with "we".
I scheduled a meeting for us in order to have a chat.
I scheduled a meeting for us to chat.
This looks and sounds fine, with or without the implied "in order to have".
I scheduled a meeting for we in order to have a chat.
I scheduled a meeting for we to chat.
This looks and sounds awful, with or without the implied "in order to have".
Attribution
Source : Link , Question Author : Cam , Answer Author : David Hammen