This is one of many Scottish surnames with an ecclesiastical background. It means servant of Jesus (Gille Iosa), which confirms that the ancestor was probably a Pict monk or a church official.
The family were followers of the MacPhersons, and the name was most common in Badenoch and the Hebrides. In 1128, a member of the Gillise family witnessed a charter granted by David I to Holyrood Abbey. Some years later, a son of Gillise witnessed another charter, relating to the Abbey of Scone (1164). More recently, Sir William Gillies (1898 - 1973) held the post of President of the Royal Scottish Academy.