SuttaCentral
With respect to this chant, might someone be able to explain roughly what it is and where it fits in / how it came to be?
On the linked page it says “(see extra booklet)”, but my searching powers have failed me and I can’t think of any other way to scratch my curiosity than ask you good folks.
Thanks! 
It’s puzzling because there isn’t anatta sutta in the canon, and what’s being chanted is not from the anatta lakkhana sutta! This maybe an introductory verse chanted before anatta lakkhana sutta, but I’m not sure because I can’t hear the text well with this accent and high pitch … not any more!
The audio in the link you shared contains respectful words chanted before a sutta is read aloud/chanted.
Yantaṃ sattehi dukkhena ñeyyaṃ anattalakkhaṇaṃ
Attavādattasaññāṇaṃ sammadeva vimocanaṃ
Sambuddho taṃ pakāsesi diṭṭhasaccāna yoginaṃ
Uttariṃ paṭivedhāya bhāvetuṃ ñāṇamuttamaṃ
Yantesaṃ diṭṭhadhammānam ñāṇenupaparikkhataṃ
Sabbāsavehi cittāni vimucciṃsu asesato
Tathā ñāṇānussārena sāsanaṃ kātumicchataṃ
Sādhūnaṃ atthasiddhatthaṃ taṃ suttantaṃ bhaṇāma se
[ solo introduction ]
All beings should take pains to understand the characteristic of
not-self, which provides matchless deliverance from self-view
and self-perception, as taught by the supreme Buddha.
This teaching is given so that those who meditate on
experienceable realities may arrive at perfect comprehension;
It is for the development of perfect understanding of these
phenomena, and for the investigation of all defiled
mind-moments.
The consequence of this practice is total deliverance, so, desirous
of bringing this teaching forth with its great benefit, let us now
recite this Sutta.
Source: Chanting-Book-Vol-2-Web.pdf (742.6 KB) (page 14-23)
Most of the older parittas and many of the commonly chanted suttas are accompanied by introductions of 1-3 gāthās. These are from an old Sri Lankan paritta collection called the Catubhāṇavāra or Mahāporit. I don’t know when or by whom the collection was compiled, but it’s post-canonical and pre-Buddhaghosa. In fact it might have been composed quite a while before Buddhaghosa because it’s clear that by his time the collection’s status was already assured. In his Vinaya Commentary Buddhaghosa includes the Catubhāṇavāra in a list of the texts that a majjhima bhikkhu (one ordained between six and ten rains) needs to have memorised in order to be freed from the obligation to live in dependence on a teacher.
Thank you so much @Gabriel_L & Ven. @Dhammanando! 
(P.S. I would mark the Q solved, but I can’t select more than one answer and both of your replies combined have led to the satisfied relief of my curiosity).
And may I add, that in recital, such introductions are a lovely piece of ritual. The Sangha sits silently as a leader begins, and if there are lay people present, it is a chance for all to settle down. Then after a few lines, the whole group joins in: very powerful!
Where can we find a full list of the suttas in that collection?
gnlaera’s link seems to be complete. Ven. Ānandajoti has published a fine scholarly edition with all the introductory verses included, along with analyses of the metres. Here.
In Thailand the four bhāṇavāras (recitation cycles) are:
First bhāṇavāra — from Saraṇagamana to Dhajaggasutta.
Second bhāṇavāra — the three Bojjhaṅgasuttas.
Third bhāṇavāra — Girimānandasutta and Isigilisutta.
Fourth bhāṇavāra — Dhammacakkappavattanasutta and Āṭānāṭiyasutta.
In Sri Lanka the divisions are:
First bhāṇavāra — from Saraṇagamana to Dhajaggasutta.
Second bhāṇavāra — from Mahākassapabojjhaṅgasutta to Saccavibhaṅgasutta.
Third bhāṇavāra — Āṭānāṭiyasutta part I.
Fourth bhāṇavāra — Āṭānāṭiyasutta part II.
The Sri Lankans chant the Āṭānāṭiyasutta in full, while the Thais usually chant a greatly abridged version.
Peter Skilling gives a general survey of Theravāda paritta sources in The Rakṣā Literature of the Śrāvakayāna, JPTS. vol. XVI pp. 116-124. Here.
It seems that he disagrees with my (and Ajahn Thanissaro’s) identification of the Catubhāṇavāramahāpirit with the suttantato cattāro bhāṇavārā referred to in Buddhaghosa’s Vinaya Commentary. Oh, well.