That is really not correct. Chain migration is what happens when we give visa preferences to relatives of immigrants already here. So someone is allowed to come in because she's a nurse and demand for nurses is very high. She then brings in her adult sister. The adult sister brings over her husband and children. The husband sponsors his siblings and their parents. They then sponsor their siblings (his aunts and uncles). The aunts and uncles sponsor their adult children. etc., etc., etc.
That is chain migration.
The newborn citizen is the ‘anchor’ for the chain.