Ah, try:
1. Create a new table called "Zip Codes"
2. In your main table, create a linked field to "Zip Codes"
3. Click the "Zip" field header in your main table so that the whole column is selected
4. Hit CMD / CTRL + C
5. In your main table, click the field header of the linked field to "Zip Codes"
6. Hit CMD / CTRL + V
  - This will create one record per unique zip code in "Zip Codes"
7. In "Zip Codes", create a "Count" field

This should do what you want I think!

Well, what do you know? Thanks! One followup, should this self update or do I need to repeat this every time I need this list? It changes everyday.I followed your instructions and I got the list I asked for, but whenI made 2 additions to the list, it did not change the new table. Is this expected and is there a way to force it to update?

By the way, I had to use Cmd V, not Cmd P. Thanks

It doesn't self update I'm afraid.  For situations like this I usually just set up an automation to handle it for me, so in your context it'd just trigger whenever the Zip lookup field is populated and the linked field isn't.   Depends on how the data's getting input into your table though

Ah, thanks for that comment about the CMD + P thing, I've fixed it in the original post!  Not sure what happened to my brain there heh