Is there a Size limitation when writing from VB -> Excel?

Dim objData as Variant
objData = <a string>
objXLWorkBook.Sheets("Sheet1").Range(<whatever>).Value = objData

If objData is a string around 200 characters long, all is fine and my
string gets written the the cell as expected. If objData is a string
around 1000 character long, I get Error number 1004
"Applicaiton-defined or object-defined error". Is there a size
limitation? I can manually enter 1000 characters into an Excel
spreadsheet just fine.