I did email Chevron customer service a couple of days ago and asked whether there is some way, but they haven't responded as yet.

As it happens (isn't it always the way!), I was in a hurry when this happened to me. If it happens when I've got plenty of spare time, I'll try various things (leading 0, trailing 0, all 0's, all 9's, etc) to see if there's something it may accept. It did occur to me afterwards that if the ZIP code field in the system is a US-specific one, it may be all 0's or all 9's or something for non-US cards. (... or it may be something which can't be entered at all at the pump, such as all spaces, or my postcode with a leading or trailing space or who knows what else.)