Chain migration gives preference to the relatives of immigrants. So an illegal alien gets here, drops a kid. The kid is a citizen. All of that kid's relatives advance to the front of the line for admission into the country. That is chain migration. And it begins with the anchor baby.
If you are not born to American parents or to people who are in the country legally then you should not be considered an American citizen. The founders relied upon no such thing.
Here is the clause of the amendment:
Amendment XIV, Section 1, Clause 1:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
One must be born here and subject to the jurisdiction of the US to be a citizen.
It is time to fix this.