Delta faucets have replaceable parts under the handle
you need to remove the handle, you will need an allen wrench of correct size
pull the handle off
next you need to unscrew the cap surrounding the stem that the handle attaches to
use a wrench(I'd wrap a towel around the cap so you don't scratch the chrome)
under this is a plastic and rubber gasket over a stainless stem
remove these and there will be two black rubber gaskets on springs where the hot & cold water enter
I'd use the allen wrench to pop these out---these are what are causing the leak
you should be able to buy these replacement parts at you local home improvement store or local Delta wholesaler
when installing these new pieces, align them on the allen wrench so you can guide them into there respective holes
they then need to be pressed down so the the rubber caps are tight on the springs and not sticking up to far (check the old ones for reference before removing them)
then install the stainless stem, it will have a slot in the side that must be aligned on a small tit inside the cavity
the plastic and rubber gasket goes on top, this has a plastic tit that must be aligned in a slot where the threads for the cap are
then slowly screw the cap on so as not to turn the stem or plastic piece
tighten with a wrench, reinstall the handle and you should be back in business