Under tunics are difficult to prove pictorially but there is evidence from high medieval sources that a shirt was worn under the upper garment.

This is also true for the early Middle Ages where shirts made of linen are documented as burial and under garments (e.g. in the tomb of Balladoole, Isle of Man).

Vikings liked to wear their shirts close to the body, whereas the slaves tended to be dressed in sack-like garments. The emphasis here was that the undergarments were still visible when the entire garment was put on. The fine fabric made wearing a woolen outer tunic more comfortable and was a welcome alternative to wool in the summer.

Further reading: Ewing, Thor: Viking Clothing, Chalford 2007.