Incidentally, this chant is included in the Divine Liturgy of St. John Chrysostom used in Eastern Rite Churches. Sort of like how the Gloria is used in the Roman Missal for the Latin Rite.
Yes indeed! It's known as the Trisagion, and it's one of the oldest invocations to the Holy Trinity. I actually went to a Ruthenian Byzantine Rite Divine Liturgy for the first time over a New Year's trip, and I was amazed over the beauty of their service. Most of the Divine Liturgy was in English, and we chanted the Trisagion. I think their version went "Holy God, Holy and Mighty, Holy and Immortal, have mercy," but it's basically the same thing.
I learned the Divine Mercy Chaplet last summer, which was due to a variety of happenings, which I think was divine intervention in my life. As a result, my prayer life is a whole lot better than what it was. My spiritual life was saved because of the Divine Mercy devotion.