The Australian Prime Minister Malcolm Turnbull gave a speech in the House of Representatives in February 2016 in which he  began with some words in the language formerly used in the Canberra region, Ngunawal.  It was apparently the first time an Australian Prime Minister had spoken in an Aboriginal language (at least in Parliament), and probably the first time that Ngunawal had been spoken in any Parliament.  The language has been almost extinct for some time. The speech is here.
The SMH carried a nice article by Michael Gordon on the preparation for this speech, of which the following is an excerpt:

The idea was simple enough. Executing it proved the hard part, involving subterfuge, lateral thinking and a collaboration that just might shape how Malcolm Turnbull confronts the twin tasks of tackling disadvantage and advancing the cause of reconciliation.
It was Alan Tudge, the Assistant Minister to the Prime Minister, who suggested Turnbull, in his first major speech on Indigenous affairs since toppling Tony Abbott, should begin in the language of the Ngunawal, the people on whose land Parliament House is built.
Turnbull liked the idea, so a staff member contacted the Australian Institute of Aboriginal and Torres Strait Islander Studies which, in turn, referred the request to the institute’s senior linguist, Doug Marmion, for advice on how to do it.
It wasn’t as simple as forwarding a set of words and arranging for some coaching on how to deliver them. The language of the Ngunawal people was almost non-existent just two years ago, having not been widely spoken for more than a century because of the impact of dispossession.
Dr Marmion discussed one form of words with Turnbull via Skype, but the Prime Minister was very particular, wanting to “acknowledge” and “pay respects” to the elders. So the linguist sought the help of Tyronne Bell and Glen Freeman, two members of the Ngaiyuriidja Ngunawal Language Group.
Problem was, he couldn’t tell them he was ringing on Turnbull’s behalf, just in case something went wrong and Turnbull took the safe option of giving the acknowledgment in English.
Soon enough, though, they were in Turnbull’s office coaching the most powerful man in the land on how to honour their people. Freeman recalls almost having to pinch himself.
“How amazing is our country that ordinary people such as us get to meet the leader in his personal space and for him to embrace what we put to him!” he says. “He picked it up so fast it surprised me. It was lovely.”
For Turnbull, the experience changed his motivation for opening his speech in Aboriginal language. “As we looked into it, we realised this whole issue of language, and language preservation and culture was so important it could be more than a mark of respect – more a statement about the importance of language and the continuity of language,” the Prime Minister told me.
Turnbull also recast the body of the speech, highlighting a commitment to spend an extra $20 million over two years on the collection of “critical cultural knowledge” and the promotion of Indigenous cultures and traditions.
That is good news for Bell, the “knowledge-holder of the Ngunawal”, and Freeman, who for the past two years, without financial assistance, have been collecting material that will bring their language back to life.
When they began, they had around 30 words. Now they have more 300 and are confident there will soon be a strong enough understanding of the language for it to be taught in Canberra schools and to adults and widely used.
Their mission, they say, is to rediscover their collective soul and reason for being. “Language is the pathway to all things involving culture and the link to our ancestors,” says Freeman. “It’s the seed to sustenance for those who follow.”
If many non-Indigenous Australians struggle to appreciate this, Dr Marmion says it is because they have a “monolingual mindset” that makes it hard for them to appreciate the value of other languages, and particularly the value of heritage languages.
“Imagine the sense of loss if you were never able to read a letter written by your grandfather, or understand a recording of your grandmother singing,” he explains.
This is why, in January 2012, the expert panel appointed by Julia Gillard recommended that any constitutional change include recognising that Aboriginal and Torres Strait Islander languages were this country’s first tongues.
Since then, the recognition debate has struggled to achieve a consensus on what form recognition should take and when the question should be put. Part of the reason for this is that Indigenous leaders believe their voices were not being heard or respected.
Turnbull’s speech was crafted to change this perception. It included a promise to be guided by the “great wisdom” of Indigenous educator Chris Sarra, who advised the new Prime Minister to “do things with us, not to us”.
To this end, Turnbull has responded to the blueprint to empower communities produced by Cape York leader Noel Pearson and several others including Sean Gordon, who represents Indigenous communities on the Central Coast of New South Wales.
The PM has embraced the idea of partnership and agreed to fund the empowerment model in eight sites and potentially others, but held back on embracing the institutional reforms proposed in the blueprint until progress is assessed in three years. This has disappointed Pearson and Gordon, but it is a start.
Moreover, Turnbull told me recognition is “achievable” next year, and has vowed to work closely with the referendum council that will report in June on how Indigenous conventions should be structured to refine the question. “The first thing is that we’ve got to come up with some words, an amendment that is meaningful for Aboriginal people and Torres Strait islanders. It’s got to speak to, it’s got to sing to them, otherwise they’ll wash their hands of it,” he said. “

 
UPDATE (2016-09-03):  And here, delivered on 31 August 2016, is the maiden speech of MHR, Ms Linda Burney, member for Barton, the first woman of Aboriginal descent to be a member of Federal Parliament.   Ms Burney speaks in part in Wiradjuri language, and the speech includes a traditional singing invocation from three be-cloaked Wiradjuri women in the public gallery.    Ms Burney is a former NSW Minister and member of the NSW Legislative Assembly, aka the “Bear Pit”, Australia’s roughest parliament.
And, now Senator Patrick Dodson, in his maiden speech, delivered on 1 September 2016, has addressed the Senate in his native Yawuru, and obtained the agreement of the President of the Senate, Senator Stephen Parry, to respond to him in Yawuru. How heart-warming it is that the President of the Senate did this. Some background here.