Huge Listbox or fast ListView

Hello,

I'm trying to present a list of items in a listbox. Until now, no problem.
But Lately the number of items has grown tremendously. I have to present
more than 35,000 lines in the list.
Most of the listboxes in Delphi don't work with more than 32,000 items.
The Listview is far too slow (the app is an on-line, paying app).

Is there a way of speeding up things or having "Huge" listboxes.

BTW the list has to have "checkboxes" for users to select items.

Any ideas?

Thanx in advance.