From Peter Heavyside – I believe the argument structure of this psalm points to a chiastic structure as follows (ESV):
A O LORD, our Lord, how majestic is your name in all the earth! (Ps 8:1a)
B You have set your glory above the heavens. Out of the mouth of babies and infants, you have established strength because of your foes, to still the enemy and the avenger (Ps 8:1b-2)
C When I look at your heavens, the work of your fingers, the moon and the stars, which you have set in place, what is man that you are mindful of him, and the son of man that you care for him? (Ps 8:3-4)
B’ Yet you have made him a little lower than the heavenly beings and crowned him with glory and honour. You have given him dominion over the works of your hands; you have put all things under his feet, all sheep and oxen, and also the beasts of the field, the birds of the heavens, and the fish of the sea, whatever passes along the paths of the seas (Ps 8:5-8)
A’ O LORD, our Lord, how majestic is your name in all the earth! (Ps 8:9)
The A-A’ pair is obvious and clearly signals the chiasm. In B-B’, the psalmist speaks of what the Lord has done and includes points of contrast and correlation. The Lord’s glory above the heavens contrasts with man being made a little lower than “the heavenly beings (’lhym)” while the strength established in babies and infants corresponds to the dominion given to man. Furthermore, the B-B’ pair clearly coheres the transcendence of God, whose glory is above the heavens, with his work towards man’s glory and honour – a principal theme of this psalm.
The centre of the chiasm is the heart of the psalm and voices the amazement and wonder of the psalmist that the creator of the heavens and earth condescends in being mindful of man. As noted, this contrast is one of the principal themes of this psalm without which the opening and closing expressions of wonder at the Lord’s majesty would have considerably weakened meaning and power.
previous post from Nigel
A (1) O YAHWEH OUR LORD, HOW EXCELLENT IS THY NAME IN ALL THE EARTH!
B (1-3) who hast set thy glory above THE HEAVENS <08064>. Out of the mouth of babes and sucklings hast thou ordained strength because of thine enemies, that thou mightest still the enemy and the avenger. When I consider thy HEAVENS <08064>,
C (3) THE WORK of thy fingers, the moon and the stars, which thou hast ordained;
D (4,5) What is man, that thou art mindful of him? and the son of man, that thou visitest him? For thou hast made him a little lower than the angels, and hast crowned him with glory and honour.
C1 (6) Thou madest him to have dominion over THE WORKS of thy hands;
B1 (6-8) thou hast put all things under his feet: All sheep and oxen, yea, and the beasts of the field; The fowl of THE AIR <08064>, and the fish of the sea, and whatsoever passeth through the paths of the seas.
A1 (9) O YAHWEH OUR LORD, HOW EXCELLENT IS THY NAME IN ALL THE EARTH!