To avoid using chemicals,dig up as much as you can, being careful not to break it off or it will grow again. Then keep a watchful eye and dig any leaves up as soon as . Can i ask why you want to kill this off? Ivy is a life saver for birds from nesting to food. And all the bugs it keeps warm in winter. Snake

Guest if, as I suspect, your ivy is growing up the house wall or another wall then cut off the trunk, trunks, as near to the soil as you can manage. Remove the ivy from the wall. Treat the stump of the ivy with something like the product on this website http://www.selections.com/GF1911/deep-root-tree-stump-killer/

Snake I hear your concerns but ivy growing in gardens is, generally, a problem. Fine in open land situations.