Sometimes this is rendered as cuidado, but I like the plural version, since these chains involve so many forms of caring. The s could also refer to how the caring happens daily.
To quote the gender wiki:
"The term ‘global care chain’ was first used by Arlie Hochschild to
refer to “a series of personal links between people across the globe
based on the paid or unpaid work of caring”.
This concept rephrases an earlier idea introduced by Rhacel Salazar
Parrenas, which she called the international division of reproductive
labor or the international transfer of caretaking. 
Hochschild first came across this idea when she read the dissertation
of Parrenas, as she had been a member of her dissertation committee at
UC Berkeley. 
In this pioneering work, a global care chain was seen to
typically involve: “An older daughter from a poor family who cares for
her siblings while her mother works as a nanny caring for the children
of a migrating nanny who, in turn, cares for the child of a family in a
rich country.”