The reason chocolate makes dogs sick is due to the component of chocolate called theobromine which is toxic to dogs but non toxic to humans.
Basically dogs cannot metabolize the theobromine fast enough like humans can so it builds up toxic levels in the dogs system which is what kills the dog overtime.
Chocolate can kill a dog eventually but usually the chocolate poisoning won't happen really quick.
For chocolate to kill a dog the dog would have to ingest at least 20mg of theobromine or more before it led to chocolate poisoning.
However if a dog just ate a bite of chocolate it's unlikely it will cause any harm or death in the dog but if a dog does ingest enough chocolate it would likely take around a few days to a week and maybe even a month before the dog actually did die from the chocolate poisoning.
The signs of a dog that has chocolate poisoning usually appear within 12 to 72 hours after the dog ate the chocolate and most commonly the dog will vomit a lot.
If you think your dog has eaten too much chocolate then you should take the dog to the vet for treatment or else the dog may get sick and die.