It depends on the breed, but also the chicken. My first batch, by 3 weeks all were fairly social and friendly. As they grew, one of the Production Reds, two of my sex links and two of my Barred Rocks LOVE to be held. They run up to the door and as I bend down they jump up on my knee.
I also have a singing Barred Rock. I have spoken of her many times. She was sneezy as a chick and got a lot of special attention. She is just the sweetest chicken ever. I would be devastated to loose her, she makes the brats worth while. LOL
My Australorps (all three!) will not let me touch them. They run at the sight of my hands. Everyone else either run's TO me, or just stands there and allow me to pick them up.
By about 3 weeks you can start to see who is going to love you, tolerate you, and run from you.