Chicken by nature are evasive of human contact as most animals and birds are. Chickens raised as pets would not tend to run away as much when the bond and the trust have already been established. They would not mind too much the stroking and the cuddling when truly acclimatized to human contact. The chicken may run to you when they know that you bring a treat but that is just as far as it usually goes.
The evasiveness is not totally lost. From time to time, even, with the best care, they would try to steer clear of people. Staying clear out of people and other animals is its natural inclination and often its only defense to survive longer. To raise chicken as pets that will follow you around, seek your company and even nap in your lap, hand raise the chicken while still a baby chick. When the chick is handled gently and treated well, good bonding results, so does trust.
Chicks are one of those gentle precocious creatures and they are fun to watch and nice to have around. They could very well eat whatever little morsels given to them and walk around after hatching. Very young chicks though will need a heat source. In place of the mother hen, that provides the heat by gathering them under the wings, you will need a lamp as their source of heat.
You will also want a place to keep them. Young chicks would fit well in a shoebox or something similar so long as there are small openings for ventilation. Stuff the box with paper towels, as they are easier to replace daily. Clip the lamp in the lip of the box and cover it with cloth to regulate the heat. Ideally, the heat inside the box should be warm to the touch but not exceed 90 deg Fahrenheit.
The chick will also need layers mash or starter mash inside the box and clean water. Provide the water in a shallow dish weighed down with pebbles to keep the water from spilling as chicks would scratch and walk about in the box. You would know if the chick in uncomfortable or hungry when they peep loudly, when not, the chick chirps contentedly. As the chick grows, food consistency will be different. Starting from a starter mash, it will need crumbles and then pellets. This is no cause for worry though as the feed is basically made of the same mixtures and components, the differences accounts for the degree of coarseness of the milling only.
As the pullets grow, it will eat just about anything that catches its interest. It will also need a dirt run, preferably a sunny spot, to take dirt baths on. For this reason, it is best to supervise its activity if you have a garden, as it would peck at grass as well as the next Begonia.
Keeping chicken as pets is great to those who love its very sociable nature.