From experience, HIDE them at the house.... I have lost mine before when I went out running. I had to go back and retrace every step and look for them in a complete panic (being a single female that lived by herself) - thankfully I found them but I will never do that again!
I only take one (house) key with me when I run in neighborhood. I usually wear it around neck with string or a shoe lace. If I'm at a park or someplace I put them in the glove box then lock the door. I have keyless entry on exploder though.
Fanny Pack!! LOL Just kidding. I see a lot of guys wearing these pouches on their arms. They wrap around the top of the arm and have a zipper. Not sure what they are called but I would imagine you might be able to fit your keys in there.
I make dog carry it (I wish I were kidding ha ha) I bought one of those ring type keychains and I loop it in to the ring on his collar (he does not even notice it). Works if you take your dog running ha ha....now if I could just figure out a way to get him to carry I-Pod
You couldn't tie a single key on your shoe when you tie your laces? (I've never tried it, and I don't run.....so apologies if that's a stupid suggestion....I just think it's what I would do.)