Which one of this sentences is correct?
Plane is landing at Chicago.
or
Plane is landing in Chicago.
Both are possible. 'At' appears to be more likely if we are thinking of the airport, 'in' if we are thinking of the town.
This particular use of "at" is likely to confuse learners.
We say "in" to refer to a city, and "at" for locations such as airports. However, because native speaker do indeed use the name of the city to refer to the airport that serves that city, as 5jj says, you can use either for this.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
It's OK to say: The plane is landing in Chicago at O'Hare International Airport.
BUT
It's not OK to say: The plane is landing at Chicago in O'Hare International Airport.
As Barb said, this is confusing for learners. The above examples help learners develop "their style" of English.
John
My english will be fine, but I don't know sometimes when me need to use "at" and "in"... and one left problem I need to increase my vocabulary
Those of us who don't know the name of the airport happily land at Chicago.