Tax implications for Backdoor IRA?

I currently have a rollover IRA, and no other traditional IRA account.

 

I'd like to open a new traditional IRA and then roll the contributions to a Roth IRA. Are there any tax implications to having a rollover IRA (that wouldn't be touched) and a separate traditional IRA where the funds would be rolled over to a Roth? Our contributions to the traditional IRA will be non-deductible and will be made with after-tax funds.