Dear Craig,

Yes, it is a true Catholic belief. God offered mankind immortality at the beginning of humanity, but it was rejected in original sin.

If Adam had eaten from the tree of life rather than the tree of the knowledge of good and evil, man's nature would have been graced to the degree that death was not to be experienced. Death is natural inasmuch as we are animals, but we are spiritual animals. Our spiritual souls now survive bodily death but were given the grace in the beginning to remain in union with the body as its form without death.

• God offered.
• We (in Adam) rejected.

The rest, literally, is history.

The Catechism of the Catholic Church, paragraph # 400 states:

The harmony in which they had found themselves, thanks to original justice, is now destroyed: the control of the soul's spiritual faculties over the body is shattered; the union of man and woman becomes subject to tensions, their relations henceforth marked by lust and domination. (cf. Genesis 3:7-16) Harmony with creation is broken: visible creation has become alien and hostile to man. (cf. Genesis 3:17,19) Because of man, creation is now subject to its bondage to decay. (Romans 8:21) Finally, the consequence explicitly foretold for this disobedience will come true: man will return to the ground, (Genesis 3:19; cf. 2:17) for out of it he was taken. Death makes its entrance into human history. (cf. Romans 5:12)

Read CCC paragraph number's 397-409 for more detail.

Peace,

Paul