Philip Schaff, in his classic work, The Creeds of Christendom: With a History and Critical Notes, Vol. 1, The History of Creeds (Grand Rapids: Baker Books, 1996), 30-34, addresses the seven key doctrinal truths related to Chalcedonian Christology. What follows is an abbreviated excerpt (emphasis his).

1. A true INCARNATION of the Logos, or the second person of the God-head . . . an actual abiding union of the two in one personal life.
2. The precise distinction between NATURE and PERSON. . . . The Logos assumed, not a human person (else we would have two persons, a divine and a human), but human nature which is common to us all; and hence he redeemed, not a particular man, but all men as partakers of the same nature.
3. The GOD-MAN as the result of the incarnation. . . . he is one person both divine and human.
4. The DUALITY OF THE NATURES. The orthodox doctrine maintains . . . the distinction of nature even after the act of incarnation, without confusion or conversion, yet, on the other hand, without division or separation, so that the divine will ever remain divine, and the human ever human, and yet the two have continually one common life, and interpenetrate each other, like the persons of the Trinity.
5. The UNITY OF THE PERSON. The union of the divine and human nature in Christ is a permanent state resulting from the incarnation, and is a real, supernatural, personal, and inseparable union. . . . The two natures constitute but one personal life, and yet remain distinct.
6. The whole WORK of Christ is to be attributed to his person, and not to the one or the other nature exclusively. The person is the acting subject, the nature the organ or medium. It is the one divine-human person of Christ that wrought the miracles by virtue of his divine nature, and that suffered through the sensorium of his human nature.
7. The ENHYPOSTASIA, of the human nature of Christ . . . . The meaning of this doctrine is that Christ’s human nature had no independent personality of its own, besides the divine, and that the divine nature is the root and basis of his personality. . . . His human personality was completed and perfected by being so incorporated with the pre-existent Logos-personality as to find in it alone its full self-consciousness, and to be permeated and controlled by it in every stage of its development.

At the conclusion of this section, Schaff addresses the strengths of this wonderfully rich Christological Creed.

This, indeed, is the peculiar excellence of the Creed of Chalcedon, that it exhibits so sure a tact and so wise a circumspection in uniting the colossal antithesis in Christ, and seeks to do justice alike to the distinction of the natures and to the unity of the person. In Christ all contradictions are reconciled.

Schaff also recognizes that this Creed consists of both that which is essential Christological truth and also the appropriate parameters or boundaries outside of which are Christological heresies. And yet these truths and parameters do not exhaust the truth of the incarnation, or our understanding of the God-man. Though we have plumbed certain Christological depths, we have only scratched the surface. For indeed, as Paul writes in one of the early Christological hymns about the incarnation, “the mystery of godliness is great” (1 Tim. 3:16).

The Chalcedonian Creed is far from exhausting the great mystery of godliness, ‘God manifest in flesh.’ It leaves much room for a fuller appreciation of the genuine, perfect, sinless humanity of Christ. . . But it indicates the essential elements of Christological truth, and the boundary-lines of Christological error.