Here is an interesting story about the medal.
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The Chapel of the Miraculous Medal in Paris
The following testimony was originally was told to me, by a sister from the Daughters of Charity a few years ago. I have recently amended the account of the testimony, when some new facts came to light. (I thank my both my original source, and the more recent source of this information.)
A mother from Brazil took her dying daughter on a trip to Paris, to visit the chapel where the apparitions of the Miraculous Medal occurred in 1830. When they arrived at the chapel, they saw a nun who was arranging flowers on the sanctuary. The mother asked her if it would be possible for her daughter to touch the chair, that our Lady had sat on while talking to Saint Catherine Labouré during one of the visions. The nun said that it was not allowed. She then went into the back room to get some more flowers. The area where the chair was, had been roped off. The mother thought to herself, “I did not come all this way, just to look at the chair.” She told her daughter to get down on the floor, work her way on her stomach under the rope, move up and quickly touch the chair and then come back. To the mother’s distress the little girl went up to the chair, and placed her head upon it, and would not come back for quite a while despite her mother’s pleading. The mother was worried that the nun would come back and that they would get into trouble. Eventually the little girl came back, and the mother asked her why she had done this. Her reply was “I am sorry mummy, but the lady told me to rest my head on her lap”. After this they returned to Brazil on the plane. Soon after their return to Brazil doctors found that the child was fully healed.
The prayer on the Miraculous Medal prayer is: “O Mary conceived without sin pray for us, who have recourse to thee”. Many favours are granted to those who wear the Miraculous Medal and who pray to Our Lady confidently trusting in her intercession. These favours include healings, protection in danger, conversions, help to fight temptations and many other needs such as employment. The feast day of the Miraculous Medal is celebrated on November 27.
From my book: Help from Heaven (Answers to prayer)