The perfect tool for this job is a pipe wrench--or, ideally, two of them. A pipe wrench is designed specifically to grip a round object tighter as you apply more tangential force. If you use the two pipe wrenches in the same manner as your router wrenches, squeezing the two handles toward each other with one or both hands, you'll be able to get the chuck at least as tight as you can get it with the key.
If you only have one pipe wrench, you can make your own hardwood wrench with bolts that fit into the key holes on the smaller part of the chuck.
You can also use a pipe wrench in place of the tongue-and-groove pliers in one of the methods mentioned in Matt's answer.
As with the tongue-and-groove pliers method described by Matt, you can wrap the two parts of the chuck with cloth or rubber to prevent marring. When possible, I use pieces of rubber cut from an old bicycle inner tube to prevent marring with my pipe wrench.
I am aware that I can buy a new key for my drill but that does not help me at this moment.
If you need to finish a project and can't wait 2 or more days to receive a key bought online, your local hardware store may stock chuck keys.
You can also post an ad for a chuck key and/or drill on your local Freecycle group, Craigslist, Facebook buy/sell/trade groups, etc., or borrow one from a neighbor or friend.