Both sentences are grammatically correct, but they have slightly different emphasis.
"The object here is the chair."
This sentence places emphasis on the location or context, indicating that the chair is the object specifically in that particular location or situation. It suggests that there may be other objects in different locations or situations.
"The object is the chair here."
This sentence places emphasis on the chair itself, highlighting that it is the object in question. It suggests that there may be other objects elsewhere, but in this specific case, the chair is the object.
So, the choice between the two sentences depends on the intended emphasis and context of the statement.