Where can I find the earliest possible version of the Mahā Karuṇā Dhāraṇī ("Great Compassion Mantra")? I am looking for the earliest possible version of the Mahā Karuṇā Dhāraṇī ("Great Compassion Mantra") in Sanskrit or Pali as part of tracing it's origins. My hope is to find the Chinese contributions. I suspect it can be found in a book, either in print or not, but entirely in Sanskrit. As I am not literate in this language it hinders my task.

Can anyone recommend where I can find such a book or source containing the text of the Mahā Karuṇā Dhāraṇī ("Great Compassion Mantra") dating before the first Chinese translation of 627 AD? Is there a library that one could recommend that would have a good chance of having it? 

Thank you so much for any help you can give.
Generally speaking the study of dhāraṇī has been sorely neglected until very recently. As such there is very little published information on the subject. For example Paul William's standard text on Mahāyāna Buddhism contains no reference to dhāraṇī.
As the article by the Lokesh Chandra says, the earliest extant texts of this particular dhāraṇī date from the 7th century Chinese translations (T1057 + Siddhaṃ). I see no sign of an independent Sanskrit text anywhere, and Chandra doesn't cite one either. So the Sanskrit texts that are floating around are from one or another of the Chinese texts. And be warned that these are almost certainly unreliable - particularly the Siddham script version (ironically).
The fact that in the text, Avalokiteśvara has already taken on some of Śiva's attributes means that it was probably composed not much earlier than the 7th century. Nīlakaṇṭha is a name of Śiva, as is Īśvara (from Avalokita-īśvara). In Alexander Studholme's book Origins of Om maṇipadme hūṃ he notes that the assimilation of Śiva into Buddhism is a theme in the Kāraṇḍavyūha Sūtra which he dates to the 4th Century CE. I suspect that it must be a century or two later than this, just before the emergence of Tantric Buddhism. So the dhāraṇī in question is certainly no earlier than the 4th or 5th century CE.
The Sanskrit text looks to be mainly classical Sanskrit. Although this could just be the bias of editors who reconstructed the Sanskrit from the Chinese! Presuming that the transcription is accurate, it also argues for a date of not earlier than the 4th century CE, since before that time Buddhist texts were composed in Prakrit. Many dhāraṇī's, such as those included in the Saddharmapuṇḍarikā and Suvarṇabhāsottama Sūtras sometime around the 4th century CE, seem to have been composed in Buddhist Hybrid Sanskrit. There never was any text like this in Pāḷi, although Gāndhārī is a possibility since many early Mahāyāna texts were composed in that language. However, very few Gāndhārī texts have been found and not all of them have been edited and published. But see for example the article by Ingo Stauch &quot;The evolution of the Buddhist rakṣā genre in the light of new evidence from Gandhāra: The Manasvi-nāgarāja-sūtra from the Bajaur Collection of Kharoṣṭhī Manuscripts&quot; in the BSOAS issue listed below
So it seems to me that you have the earliest text already and that looking for the &quot;original&quot; is probably not going to turn up any more information.
A couple of publications that you might want check are:

Copp, Paul. (2014) The Body Incantatory: Spells and the Ritual Imagination in Medieval Chinese Buddhism. Columbia University Press.
Studholme, Alexander (2002). The origins of oṃ manipadme hūṃ: a study of the Kāraṇḍavyūha Sūtra. Albany: State university of New York Press.

Also if you can get hold of it the Bulletin of the School of Oriental and African Studies, Volume 77 - Issue 01 - February 2014. The contents page is available here, and as you will see it has many articles on dhāraṇī.
There may be info in Esoteric Buddhism and the Tantras in East Asia
edited by Charles Orzech, Henrik Sørensen, Richard Payne. I don't have it to hand and the Google Books version has no previews, though the word nīlakaṇṭha is mentioned several times.