not being funny but are you sure its the chain?
The z22se has been known to have noisey hydraulic tappets or a blowing exhaust manifold both can sound pretty noisey when it starts.
next cold start, pop the bonnet and get someone else to start the car whilst you listen. It should be obvious if the rattle is coming from the chain area or not.
Also ring up whoever serviced it and ask if they have a record of changing the chain. I did that and they were very helpful. 😃