[Legolas]

Altering the CCR5 gene does have potential, though I wouldn't hold my breath for a cure just yet.
Note: I could be wrong about any of the below:

What happens normally is that your bone marrow produces cells for your immune system as well as red blood cells for moving oxygen through your blood and platelets to stop your bleeding.
Some of those cells supporting the immune system, mainly the T4-helper cells, are used by the HIV as hosts in which they can multiply. Together with some other tinkering, the disruption of those cells is what eventually causes the immune deficiency - you'll generally have enough HIV in your body to cause problems after 9 years or so.

One of the problems with HIV is that it changes its outward appearance rather a lot. That means it's hard to detect directly, and hard to target specifically with medication.
What doesn't change as much is the core mechanism. By blocking one or more parts of how it finds, enters, multiplies within or leaves a T4 cell you can keep the virus in check.
In the article, they suggest a way to prevent the entry.

Before the virus will try to enter a cell, it has to bump into a couple of receptors it recognizes, like keyholes it has keys to.
For the majority of HIV, one of those co-receptors is CCD5. Another kind uses CXCR4 instead, and there are doubtless other, rarer sorts as well.
CCD5 is also found on other cells playing a part in HIV-1 pathogenesis, like macrophages and dendritic cells.
Of course, the receptor isn't just there to help HIV along but responds to other substances that do belong in your body. Having a lot of those (or artificial variants) means they compete with HIV for available space and while that doesn't block access entirely it can add two years or so to the incubation time.

What's interesting about the CCD5 receptor is that we know there is an uncommon mutation which makes people immune to most HIV infections (called CCR5-Δ32), found mainly in northern Europe. Disabling the receptor that way doesn't seem to have a major impact on one's life, except perhaps that you run a bigger risk of catching something like the West Nile virus instead.

So far so good. But unless you've gotten that mutation from both of your parents, each cell in your body has at least one and probably two CCD5 genes that can tell you how to make proper T-cells, macrophages and so on. If you change some of them, the rest will keep on making suitable HIV hosts.
Luckily, not every cell makes every receptor protein locked inside your genes. For this one we can pretty much narrow it down to the bone marrow.
Which is another stroke of fortune, because bone marrow cells are very easy to find. Unlike most of the rest of your cells they're very active because they have to keep renewing your blood and immune system.

There are two ways to change them. The one used in the article is to destroy the ones you have using cancer medication, after which you are injected with new ones that will hopefully move to the right place and start working before you die of an infection or excessive bleeding. Because the bone marrow cells come from another person, there's always the risk of your body rejecting the cells at which point you're really in trouble.
Bone marrow transplants are definitely not for everyone, but if your aids inhibitors aren't getting the job done and you qualify and you have a suitable donor it might help.

The other is through gene therapy. The idea there is that you send a bit of DNA to your bone marrow cells to change the CCD5 gene so you get a different CCD5 receptor in your T4 cells. Nothing stops working meanwhile, so it would be a much kinder approach.
The difficulty there is that you need to get that information to virtually all of your bone marrow cells, and to their DNA, and to the right place in that DNA, and safely.
One of the most promising approaches for that ironically involves a retrovirus much like HIV itself, though nowhere near as harmful. Optimizing such a process takes a lot of work though so we're not there yet.

While a transplantation or gene therapy doesn't eliminate HIV in itself, it does keep it from multiplying, and one of the single biggest benefits is that it does so without your needing to take medication on a regular basis.
It's easy to see why gene therapy is such a promising field of research, but at the same time the body is such a complex thing there are many challenges to overcome - and public opinion is just one more.