The Chariot Arcana
The Chariot Arcana in Persona 3 can be started and finished pretty early on in the game. You start it by speaking with Kazushi Miyamoto in your class room and joining the Kendo team with him. This one was one of the more difficult ones for me to raise since I always picked the wrong answers in convo. You pretty much just need to keep telling Kazushi not to be a bitch and suck up the pain.
You will meet two different Social Links through raising the Chariot Arcana. The first of which is Yuko who is tied to the Strength Social Link. You meet her very early on as she is the coach of the Kendo team. Way later during this Social Link (during the sports competition between schools) you'll meet Mamoru Hayase as well who is tied to the Star Social Link. Note that all you have to do is attend the sports competition to meet Mamoru.
When you max out the Chariot Social Link you'll be able to create the Persona, Thor which is actually one of the more powerful Lightning using Personas in the game.
While raising a Social Link you'll be given story cutscenes where you'll have to answer questions. The answers to each of these questions is different depending on the person and the situation. What you usually need to try and do is pick an answer that reflects their personality. Here's a cheat sheet for each Social Link rank of the Chariot Arcana and what to say.
Rank 1: Automatically gained
Rank 2: Tell him to "Toughen Up" - anything - anything
Rank 3: Are you sure you're ok? - Will it heal?
Rank 4: Anything - that sucks
Rank 5: The hospital again? - (Let him use your shoulder for support)
Rank 6: Suck it up - Is it that important? - What will happen to your knee?
Rank 7: How is your knee? - You need to toughen up
Rank 8: Look Away
Rank 9: I'm fine
Rank 10: Automatically earned
Upon completion of the Chariot Social Link you'll be able to fuse Thor through regular or triangular fusion. Thor is required for Request 65 in Persona 3 FES.