Check gmail Accounts & Import settings on the gmail site to see if it's collecting mail from Charter, and check Charter webmail to see if it's set to forward to gmail.

There was a setting in gmail to send mail as the charter account. I have removed that to see what happens. Thanks for that tip. Charter was not set to forward any mail. I'll update once I see what happens.

that doesn't seem to have helped. I'm still seeing the email arrive in the Charter inbox and then a few minutes later appear in the gmail one. It is interesting that the TO: is still the charter email address even if it is in the gmail.com box.

The gmail setting you changed just allows you to send from the Charter account, through the gmail smtp, without gmail switching out the Charter address with the gmail one. So, recipients see your mail being sent from Charter instead of gmail. The 'Check mail from other account' setting is where gmail could collect Charter mail.

I deleted my charter account from the check mail from other account. But it didn't help. I am still seeing emails on both accounts. I also double checked the settings on Charter. Mail forwarding is turned off.