Connection time in Dublin Airport

Which airline(s)?

Dublin airport is small so 55 minutes should be enough IF you arrive on time and whiz through the arrival process. Personally I'd like to have some more time.

I used Dublin as a hub from Atlanta to Paris a couple of years ago and 55 minutes wouldn't have been enough. There's a lot of info missing from your question so you may be good depending on where you are flying out of and if you are checked through on the same airline. We had to switch terminals as we were coming from the U.S. and this took some time as it was early and the tram wasn't running so we had to walk. No biggie but added some time. If you are returning on the same leg, make sure you have at least 3 hours in Dublin. Customs was a nightmare and we used every minute of three hours to get to the gate.

We will flying from Lexington Kentucky, USA via Chicago O'Hare via Dublin to Frankfurt.
We have a two and half hour layover in Chicago, a fifty five minute layover in Dublin and then on into Frankfurt. We will be flying Aer Lingus. On our return flights there is no problem, as we have four hour layovers in Dublin and in Chicago.
Thanks for you input.
Ben

Take the transfer corridor and you should be fine. This bypasses the regular immigration queue but you will still go through a passport check and security. The only transfers that avoid this are those that happen to both use the 300 gates which won't be your situation.