The Council of Chalcedon (451) Implicitly Accepts the Filioque: The De Trinitate of St. Hilary of Poitiers (+367)
In the 1st Session of the Council of Chalcedon (451), the following is recorded in the Acts accepted by both the Greek and Latin bishops:
"The most glorious judges and the whole senate said; Let each one of the most reverend bishops of the present synod, hasten to set forth how he believes, writing without any fear, but placing the fear of God before his eyes; knowing that our most divine and pious lord believes according to the ecthesis of the three hundred and eighteen holy fathers at Nice, and according to the ecthesis of the one hundred and fifty after them, and according to the Canonical epistles and ectheses of the holy fathers Gregory, Basil, Athanasius, Hilary, Ambrose, and according to the two canonical epistles of Cyril, which were confirmed and published in the first Council of Ephesus, nor does he in any point depart from the faith of the same." (Source)
Here we have an ecumenical council shelving the"ectheses", i.e., plural form of θέσῐς (thesis) which in Greek is θέσεις or thesēs in Latin, of certain Church Fathers together with the rule of the decrees of prior ecumenical councils. The theological writings of the Cappadocians, Athanasius, Hilary of Poitiers, and Ambrose of Milan are next to irrefutable according to the mind of the Council, and therefore the mind of the Church, the mind of the Spirit, the mind of Christ, and the mind of God the Father.
One of the most prominent works of St. Hilary is his De Trinitate (On the Trinity). It would be absurd to think that the Council of Chalcedon can put Hilary on the shelf with Nicaea 325, Ephesus 431, and other Nicene heroes (Gregory Nazianzen, Gregory of Nyssa, Basil the Great, Athanasius the Great, Ambrose of Milan, and Cyril of Alexandria) and yet reject his work on the Holy Trinity.
However, St. Hilary of Poitiers is a well-known supporter of the belief that the Holy Spirit has His eternal origin from the Father and the Son. In each of these passages, it is upheld that the Spirit is from the Father through the Son (in his hypostatic origination, which is condemned by the Eastern Orthodox Church) or that He receives the divine nature/essence (power, teaching, excellence, etc., etc.) from the Son (ultimately from the Father). Let's look at these passages in context:
"Concerning the Holy Spirit I ought not to be silent, and yet I have no need to speak; still, for the sake of those who are in ignorance, I cannot refrain. There is no need to speak because we are bound to confess Him, proceeding, as He does, from the Father and the Son (qui Patre et Filio auctoribus, confitendus est)."De Trinitate, 2.29 (New Advent)
and
"Your Holy Spirit, as the Apostle says, searches and knows Your deep things, and as Intercessor for me speaks to You words I could not utter; and shall I express or rather dishonour, by the title 'creature,' the power of His nature, which subsists eternally, derived from You through Your Only-begotten (naturae suae ex te per unigenitum tuum manentis potentiam creationis nomine non modo eloquar, sed etiam infamabo)?" De Trinitate 12.55 (New Advent); [PL 10, 469B-70A]
and
[...] Let me, in short, adore You our Father, and Your Son together with You; let me win the favour of Your Holy Spirit, Who is from You, through Your Only-begotten (ex te per eum sanctus Spiritus tuus est). For I have a convincing Witness to my faith, Who says, 'Father, all Mine are Yours, and Yours are Mine'”. De Trinitate 12.57 (New Advent); [PL 10, 469B-70A]
And finally:
“For the present I forbear to expose their licence of speculation, some of them holding that the Paraclete Spirit comes from the Father or from the Son. For our Lord has not left this in uncertainty, for after these same words He spoke thus — 'I have yet many things to say unto you, but you cannot bear them now. When He, the Spirit of truth, has come, He shall guide you into all truth: for He shall not speak from Himself: but whatever things He shall hear, these shall He speak; and He shall declare unto you the things that are to come. He shall glorify Me: for He shall receive of Mine and shall declare it unto you. All things whatsoever the Father has are Mine: therefore said I, He shall receive of Mine and shall declare it unto you.' Accordingly He receives from the Son, Who is both sent by Him, and proceeds from the Father. Now I ask whether to receive from the Son is the same thing as to proceed from the Father. But if one believes that there is a difference between receiving from the Son and proceeding from the Father, surely to receive from the Son and to receive from the Father will be regarded as one and the same thing. For our Lord Himself says, 'Because He shall receive of Mine and shall declare it unto you. All things whatsoever the Father has are Mine: therefore said I, He shall receive of Mine and shall declare it unto you.' That which He will receive — whether it will be power, or excellence, or teaching — the Son has said must be received from Him, and again He indicates that this same thing must be received from the Father. For when He says that all things whatsoever the Father has are His, and that for this cause He declared that it must be received from His own, He teaches also that what is received from the Father is yet received from Himself, because all things that the Father has are His. Such a unity admits no difference, nor does it make any difference from whom that is received, which given by the Father is described as given by the Son. [...] that because all things which the Father has are His, therefore the Spirit of truth shall receive of Him — is to be referred to unity of nature." De Trinitate 8.20 (New Advent); [PL 10, 250C-2A]