but the first flight (lga-chi) to catch my chi tlv flight is considered domestic....
YMMV but when I've taken such flights I've gotten them to check it for free since they were checking it all the way and I was allowed one piece. You're flying Delta the whole way, correct? If so you should for sure be fine IMHO.
I have the same thing catching my ELAL/AA flight this week though I'm not flying AA to NY so we'll see what happens. Hoping Delta won't give me problems.