Instructions
Place Chansey on your Pokemon team instead of keeping him in the PC. The longer Chansey is on your active team, the happier he will be.
Give Chansey plenty of vitamins, which you can buy from Pokemarts throughout the game, such as the one in Slateport City. Vitamins include calcium, iron, carbos, protein and zinc.
Go to the massage parlor in Veilstone City, which is located just below the Gym. Talk to the lady inside and she will offer to massage one of your Pokemon. Select Chansey as the Pokemon you'd like to have her massage. Note that you can only do this once per day.
Check to see how happy your Chansey is by talking to the woman in Verdanturf Town who lives in the building next to Wanda's house. If she says, "It adores you. It can't possibly love you any more. I even feel happy seeing it," Chansey has reached the maximum happiness and will evolve into Blissey the next time he gains a level.