First off, quick clarification: "chiral" simply means distinct from its mirror image. All current life is chiral, in that it is made up of molecules which have a "handedness". What you're asking about is life which is made up of molecules of the opposite handedness (which I'll term "mirror chiral").
Such a lifeform is theoretically possible - chemical and biological reactions and reaction rates are entirely the same between the two handednesses - presuming that all participants (substrates, products, catalysts, etc.) are flipped to the opposite chirality. A mirror chiral Jarek would look and function exactly like the normal chirality Jarek, although he would need to eat mirror chiral food instead of normal chirality food.
So what difficulties would you have to synthesize a mirror chiral organism? The biggest one is the bootstrapping issue. There's a large suite of molecules in the cell which are all needed in order to replicate the cell, or even just maintain it. All of these need to be present in order for the organism to work. The organism can make all these components from scratch, but to do so it already needs to have these components.
Synthetic organisms - that is, organisms with a genome assembled in a computer and synthesized abiologically - have been made. The trick, though, was that the synthetic DNA was then placed into already existing organisms to be replicated and to have its genes expressed. There's no limitation (besides perhaps cost) to synthesizing mirror-chirality DNA - the same machines which synthesize normal chirality DNA can do it if you swap out the reagent bottles. But what do you do with it once you have it? There's no existing mirror-chiral organisms you can place it in to replicate and express the genes.
If one was to make mirror-chiral organisms, you would need to synthesize all of the necessary cellular components in their mirror-image form. So you would need mirror RNA polymerase, mirror ribosomes, mirror t-RNA, mirror ... If you do things right you can skip most of the cellular components, but you still need a large number of them.
This is not necessarily a pipe dream. Last I knew, the J. Craig Venter Institute, the people who made the first synthetic DNA organism, are actively looking into it. The trick is to trim things down to the bare minimal number of chiral components needed to bootstrap the system. That's (more-or-less) where their current efforts are focused, from what I understand: what's the minimal number of genes needed for a viable cell? Which of these are needed to "bootstrap" a cell from bare DNA?
Personally, I'm pretty confident that a mirror-chiral organism will be created one day. The time frame for this is a little unclear, but there's nothing theoretically limiting it. The biggest issue is our current technical limits in synthesizing sufficient quantities of (non-DNA) biomolecules in a chemical (abiological) fashion. But those are constantly improving, and with additional research into what's needed for bootstrapping a synthetic cell, we'll push down the requirements even further.
Of course, the first mirror-chiral organism will be pretty simple. It's going to be less complex than even E. coli. It will also need to be fed a diet of (expensive) mirror-chiral food (amino acids, sugars), so its use will be limited as well.
