Our very concept of purpose is flawed; a relic of evolution. We do X to obtain Y, where Y is somehow either beneficial to survival, or at least appeals to a survival instinct or emotion. 'Y' doesn't have any true significance; it is merely a means to keep the organic machinations of our body functioning in order to facilitate our ability to breed. 'Y' is purposeless. This purposelessness is inherent in both mortal and immortal life – an endless string of 'Y's is carries [sic] no more purpose than a finite number of them.
[NB: Although I am addressing these words to this commenter, I am also, of course, writing for all eyes. The "you" is simultaneously a personal and a general. Spoky, innit?]
I'm sorry but I need you to provide a better theoretical context for your claims, otherwise all I'm hearing is pops and buzzes, little more than neo-Darwinian nonsense. I think you've missed a subtle, but basic, philosophical point about teleology. To wit, the most austere, fundamental element of (Christian) teleology is that contingent acts have an intrinsic capacity to achieve certain ends. You may disagree human teeth were designed (in any meaingful sense of the word) for the purpose of eating. But I think you're much harder pressed to ddeny teeth function for the purpose of eating. All effective means are inherently teleological. (The classical idea of the teleological argument, and its intuitive durability, is that the overwhelming prevalence of all this purposeful activity - leaving aside for the moment whether its divinely designed or not - suggests very strongly there is some kind of higher order to the world.) To use your variables, you may coherently claim Y is a useless, worthless end (as you seem to say in your final words), but you the reason you cannot say X is a purposeless act is *precisely because* it achieves Y.
The basic problem is that you seem to be confusing micro-level teleology with macro-level teleology. (The same error occurs when people run wild with "quantum indeterminacy," as if it exploded the obvious integrity of causality at all higher levels; or when people hastily assume micro-evolution seamlessly entails macro-evolution.) Though you fail to realize it, the X-Y scenario you provide in fact completely validates the former kind of teleology. As I said, X is purposeful precisely because it achieves Y. X has an intrinsic teleological aim towards Y. More than that, Y is also purposeful precisely because it, too, aims at and achieves a greater good: namely, as you say, the sustenance of an organism (let's call it Z). But in neither case do you have grounds to deny the teleology of X and Y.
What you must address, now more on a moral than metaphysical level, is that some acts, some Y's, have infinite value *in themselves*, even apart from their attainment. Y is good because it is an increase, or at least maintenance of being itself. This maintenance -- this "letting it BE!" -- is inherently a Good Thing by virtue of the fact that all being and all beings partake of God, who is pure Goodness, pure Being. And, contrary to your melancholy chain analogy, because Y or any other intrinsically good things are Good Things, even a single link of it outweighs an infinite chains of worthless things. It's a shame, a tragedy, really, that you seem to focus on the boring, futile poverty of life when so many other people are gasping for a taste of such a lush wasteland.
Perhaps sensing this, you all of a sudden make a final murderous leap at the throat of macro-level teleology -- "ultimate purpose" -- as if to justify the purposelessness you see in life. But you are left simply asserting organic life and health are vanity, all vanity. Unfortunately, however, not only does your own life contradict this seemingly stoical, sober, all-is-vanity attitude at the most intimate levels -- how long do you hold out when your body, or any other thing of great value, whimpers for help? -- not only this, but also leading thinkers have a beef with a totally purposeless view of the world at the highest theoretical levels. Specifically, I encourage you to read (among countless similar and related books) Michael Denton's _Nature's Destiny: How the Laws of Biology Reveal Purpose in the Universe_, Dean Overman's _A Case Against Accident and Self-Organization_, Micheal Behe's _Darwin's Black Box_, Dennis Bonnette's Origin of the Human Species, and (if you could ever get your hands on a less than exorbitant copy!) Etienne Gilson's _From Aristotle to Darwin and Back Again_. In the meantime, I offer some of my own brief, paltry thoughts on these matters.
It may be small or no consolation for me to say, as a Christian, I too know the sense of purposelessness life often shoves in our faces. Insofar as Christians are not immune from any sin, we are not immune from the sin of despair. Make no mistake: despair is a sin; but hope is a blessing. Hope is a gift of grace, not the natural fruit of casual human observation. Faith is a gift, and hope in the Risen Christ is the fruit of faith. Hope is the only antidote to the poison of aimless despair.
So, hey, I openly admit purpose is often very difficult to see in my life. Sometimes I do ask, "Why Y?" But then, despite myself, with God's unexpected grace of insight, I stumble into a reverie of hindsight and realize, with a leap of heart and a prayer of thanks, why God ordered my life the way He had up to that "moment of clarity."