In addition to Jonathan's point, it's worth noting that the tensioner requires oil pressure to do its thing. It takes several cranks of the engine to build up enough oil pressure for that tensioner rail to come out, and as the pressure falls away the rail will retreat into the rest position. So even after you have replaced your chain you may still see some slack when everything is at rest.

This is why, after changing the oil, it is so important to crank the engine over with a disabled coil for 25-30 seconds to build up healthy oil pressure. We don't want that slack to bunch up under a rail or cause us to jump time.