Part of the pipe in my chimney broke off inside how do i get it out?

the furnace guys looked at the chimney and said that part of the terracotta pipe broke off inside the chimney and it is causing problems with the venting for the furnace. if anyone has any ideas on what would be the best way to fix this problem. We don't use the furnace like normal its only a back up for our heat but still may have to use it from time to time so i want to also know is it safe to use after we get the piece out of the chimney. please help don't have the money to replace the chimney so hoping to fix for now..