You can let your freshly killed chicken sit in your fridge for a while, as long as you keep it cold. A week will not hurt it.
I have had fresh meat in my fridge for 2 1/2 weeks and it was still good (it was an oops, not a planned thing). No smell, no off taste, no one got sick or died. It actually tasted great and I kept the leftovers for over a week.
The chicken you get from the store has been hanging around for a while before it ever hits the meat counter. When I worked at a small grocery store during high school, we got meat shipments once a week, and it would sit in the cooler until the butcher needed it to fill the case, some was in there for 9 days before being used. Then they date it for X number of days from when they clean/cut/wrap it for purchase. The last day they can sell it, they would sticker it for "Manager Special" to sell it quick before they had to toss it.
Also, it took me 5 days to thaw a 18 pound turkey, using the recommendation on the package.