No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Is Amex the best move then? Get a little more credit with Discover and a competitor and then let Chase join the party? I checked my one free report from EX and it showed Chase SP'ed me. That has to be good news?
Amex Everyday is my suggestion!
I would search for an Amex Charge Card (like PRG) 50k offer through creditcards. If approved, immediately (same day) app for an Amex revolver card like Everyday. Many people have been able to get both with 1 hard pull.
Jamesdwi is right, give it a few more months before you go for Chase. They seem to like 12 months of history on existing accts.