The Chin Rest is normally held on by rotating the two tube nuts which have a small hole at the midpoint.
The nuts are turned using suitable stiff metal pin (e.g. large paperclip). Open the clamp this way while off the violin, then replace taking care not to scratch the ribs.
The Tube Nuts each have a right and left-hand thread which provides the clamp action.
CAUTION do not unscew completely.
Alan.G, October 2016