Why do some Catholics wear little chains around their wrists?

At the end of St. Louis de Montfort's True Devotion to Mary, he suggests the wearing of little chains to remind a person of their consecration to Jesus through Mary.

It is not a requirement of the devotion, as he notes, "It is perfectly true, these external tokens are not essential and may very well be dispensed with by those who have made this consecration. Nevertheless, I cannot help but give the warmest approval to those who wear them."

He then proceeds to list several reasons why the wearing of little chains can benefit a person's soul consecrated to Jesus through Mary.

While many wear these little chains on their wrists, some wear them underneath their socks around their ankles, or others may wear a more stylized chain as a necklace.

Simply put, the chain is an outward reminder of a person's commitment to live a life of holiness, ensuring that they do not forget the promises they made to God.