There was an unexpected arrival on the 3.04pm rail service from Galway to Dublin yesterday.
The woman went into labour shortly after the train left Galway.
After the alarm was raised, the train stopped at Kildare Station at around 5pm and emergency services were notified.
A part of the carriage was sectioned off to ensure privacy for the woman and she gave birth in the area in between carriages.
Glass doors were locked by staff and Irish Rail employees held up a blanket to protect her privacy.
Ambulance services later arrived and helped to deliver the baby on board with the assistance of an off-duty doctor who was travelling on the train, and other passengers who were medically-trained.
The baby and mother were taken to the Coombe Hospital are both said to be doing well.