After having to look this up a third time, I found a post on Vonnie’s blog about it. I made a copy here.
In short, Microsoft fucked up and you’re left with the command line to do this, unless the wireless network is in range.
The following commands list all the WIFI networks you have stored, and removes the one called “Old Network”:
netsh wlan show profiles netsh wlan delete profile name="Old Network"
See Vonnie’s blog for more details.