As always the answer is, it depends... It sounds like you're using a multiline editbox for the chat history, which could be a poor choice. Generally people chose a Listbox of some kind for this, with each line being it's own item. Using this approach, I believe, the non-visible strings (listbox items) are rejected quickly, so you may get better performance overall. There's also the possibility of managing the text yourself and setting a sub-string to be drawn rather than the entire text, I've not tried this and it sounds expensive
Also be aware that in the 0.6.x and earlier releases, rendering large amounts of text can be expensive due to the nature of what the text is, and how it's represented from a geometry point of view. Typically a 'page' of text results in many tens of thousands - even hundreds of thousands - of triangles to be drawn, which clearly has an impact on performance. We have reduced this issue in the upcoming 0.7.0 release by allowing content to be cached to texture first, meaning that after the first render of any amount of text in a suitably initialised window, it's only ever two triangles (the only time it would not give better performance is if you were modifying the text many times each second - which given your description, you will not be (generally, people don't type that quickly!).
CE.