It has been brought to my attention- a comment below is re-printed here- that this is not Dalai Lama. So, ignore all reference to Dalai Lama. The rest is okay, I think.
Sorry to say, but this was not the Dalai Lama chanting, but was a recording done by a Dutch performer called Hein Braat, and the original can be bought as a CD. It’s an urban myth which has been doing the tour for 20 years (but you’re by all means not alone in believing it!).
That doesn’t take away from just how special a piece of music it is, but the chant is from the Veda, which is not buddhist, but hindu. Tri-ambaka-m is the three-eyed one e.g. Lord Shiva.
The original recording by Hein Braat can be heard at the following link. Credit where it’s due, as he has an amazing voice.
Close your eyes, listen. Feel your heart beating,
your breath rising and falling. Do nothing.
Maha Mritvuniava Mantra
Om Tryambakam yajamah
Sugandhim pushti vardhanam
Mrityor mukshiya mamritat
Translation: I meditate on, and surrender myself to, the Divine Being who embodies the power of will, the power of knowledge, and the power of action. I pray to the Divine Being who manifests in the form of fragrance in the flower of life and is the eternal nourisher of the plant of life. like a skillful gardener, may the Lord of Life disentangle me from the binding forces of my physical, psychological, and spiritual foes. May the lord of Immortality residing within me free me from death, decay and sickness and unite me with immortality.
Explanation: This is a healing and nourishing mantra and is in a sense, “the Heart of Vedas.” The healing force awakened by this mantra sends forth its
ripples from body to psyche and from psyche to soul. It strengthens our powers of will, knowledge and action, thus unblocking the flow of enthusiasm, courage and determination. The vibration of this mantra awakens the internal healing force while attracting nature’s healing agents, creating an environment where the forces from both origins converge. This mantra connects us to the healer within and helps us receive the full nourishment from food, herbs, or any discipline undertaken for our total well being.