First of all read these Pokédex entries of Chansey from various games,
A gentle and kindhearted POKéMON that shares its nutritious eggs if it sees an injured POKéMON.
People try to catch it for its extremely nutritious eggs, but it rarely can be found.
CHANSEY lays nutritionally excellent eggs on an everyday basis. The eggs are so delicious, they are easily and eagerly devoured by even those people who have lost their appetite.
It lays several eggs a day and won’t share them with those who have evil in their hearts.
Black/White, Black 2/White 2
A kindly Pokémon that lays highly nutritious eggs and shares them with injured Pokémon or people.
The egg Chansey carries is not only delicious but also packed with nutrition. It’s used as a high-class cooking ingredient.
From its Pokédex entries in most of the games, we can assume that, Chansey's eggs are very nutritious and delicious. It doesn't share their eggs to evil people. It's eggs are capable of curing injuries, diseases. Thus, bringing happiness to the hearts of every living beings. And, It's eggs are pretty rare hence people tries to search for it. The entry from Sw/Sh makes us more aware about its medicinal value.