I say go for it!
I just got the same card yesterday.
Here is a little history so you can see how, if at all my credit worthiness may be similar to you (In the eyes of AMEX at least):
I found this site 3 years ago when I was interested in re-habing my credit. Most of my collections and chargeoffs were quite old, I paid for delete the ones I could and let the others drop off. On 1/31 I applied for a Wells Fargo Visa card and was approved with a limit of $1500. I haven't had any lines of credit in years, the only thing on my Experian report was a closed cc account from 2002 (turn's out this helps because it raises my AAoA, TU and EQ don't show this account and my score is lower). At the time I applied for the Visa 1/31 Experian wasn't even generating a score for me but there was nothing bad on my report.
I had originally applied for the AMEX Green Charge card on 2/1 and was declined. The reason given:
"We have been unable to obtain your consumer credit bureau score from the agency (ies) identified below."
"No undisputed tradelines exist with a status date or a balance within the last 6 months. (Experian)"
I then signed up for Experians "credit watch" or whatever they call their pay per month membership. I got an "alert" from them after my WF account posted for the first time, so I logged into their site and generated a report. It was now reporting a "Fako" score of 765 for me. I then called AMEX and gave them the "tracking number" that was associated wit the denial I had received on 2/1. I was connected to as CS rep and basically explained that Experian now was reporting a tradeline and score. I asked if I could reapply or have them take another look at my application now that my circumstances had changed. I also asked if it was wise given I had initially applied only 5 weeks earlier, he assured me that it wouldn't have a negative impact on their decision. So after answering some basic questions, identity related, income, if I had a checking/savings/retirement account, and then calling my bank to verify my address I was approved over the phone for the Green Charge Card.
I then asked if I could apply for a credit card. I was concerned that having just got the charge card I would have to wait some predetermined amount of time before getting a second line of credit with them. The CS rep then told me it would not be viewed negatively, and could only help my chances seeing as he was able to approve the charge card on the spot. After he read through the terms of the card I was approved again instantly. I was only given a CL of $1000 but the CS rep told me it was a result of being a new customer and lack of existing credit history. He also encouraged me to apply for an increase after 60 days.
So long story short, I got approved!
TU 672, EQ 675, EX "fako" 765
3-4 Hard inq, Income ~35k
AAoA for TU and EQ 2mo, EX 5y6mo
Seeing as you are a charge card member already as long as you have always been in good standing with them I'd bet you get approved.
Starting Score: EQ 599, TU 577
