Not at all possible. Even with video. (One caveat only applies.) Even with futuristic technology. You're still dealing with the totally unfuturistic human body. And that's something the other autosurgery answers fail to deal with.
Human arms and hands aren't designed to work behind our backs all that well. Especially when away from direct visualisation. She will need not only finger dexterity to do this job but also main strength and range of motion that will be severely curtailed for hours.
Other answers have focused on abdominal / ventral autosurgeries. Yes, those are possible, and are relatively simple procedures: you can see what you're doing and are not putting strain on your arms and your hands are working in their natural anatomic position. A c-section takes something like 20 minutes. An appendectomy can take as little 5 minutes.
None of them address the specific needs of spine surgery. The kind of surgery your character will have to do will require several hours of preparation and actual work -- if she were an actual surgeon working in an actual hospital setting. I know you've accepted one of those answers, but the reality is that your scenario simply is not going to happen.
This is a typical spinal surgery set-up.
In order to access the nerves to connect the chip, your character will need to make an incision. Incisions bleed, so she will need to achieve hemostasis. She will need to carefully dissect through two or three inches of subcutaneous tissue: muscles, connective tissue. You know, stuff that she's going to need in order to move her body around after the procedure!
This is what it looks like when dissected down to the connective tissue on the spine itself.
Once she gets down to bone, she'll still be a good inch to inch and a half away from the spinal cord itself. She will need a powered drill with several different kinds of specialised bits; she will need (quite literally!) a hammer and some chisels; she will need rongeurs. She's got to basically dig a hole through the bone in order to access the spinal cord.
Once she gets through the bone, she's going to be confronted by the dura mater, which is the layer of tissue that protects the spinal cord and contains her cerebrospinal fluid. This is the same layer of tissue and fluid that surrounds & bathes the brain. She's going to have to be very careful when dissecting bone off the dura. It's very easy to tear!
View of the spinal cord itself.
Once she makes the incision through the dura, she'll at last be down to the spinal cord. Yay! That is the nerve that connects to her brain. Everything she's done so far is basically preparation for seating the implant. The "chip". At this point, she will have to know where in that mass of neurons is the appropriate nerve for the "chip" to be connected to. Easy-peasy!
Once the implant is in place, she's off the hook, right!?
She's still got to extricate herself from the situation. She has to close each and every layer that she just butchered in order to get down to the spinal cord. She will need to very carefully sew her own dura mater closed using extremely thin sutures and long specially designed needle holders.
Once that's done, she's gong to need to take all those bone chunks, mix them up with some blood and allograft bone chips in order to make a kind of bony bandage over the hole she made.
Stitches and glue.
And then she'll have to secure the implant itself to her spine so it won't move around and come loose. She does NOT want to create a CSF leak where the "chip" attaches to her spinal cord! This will involve another drill which she'll use to shape a pocket in her spinal column so that the "chip" will have a secure home. And then a much smaller drill and a bunch of fiddly little screws to secure the implant to the bone.
Then she'll have to close up the layers of muscle and tendons, subcutaneous layers and skin. If she's lucky, she'll end up with a nice little scar.
Basically, all you're asking your character to do is be not only an orthopedic surgeon (for the bone work) but also a neurosurgeon (for the nerve work and implantation) but to do all this whilst wide awake and alert! Sorry, but a little 0.5% novocaine is not going to get her through this.
Spine surgery is brutal. It requires great physical strength to do the dissections and to get through the bone. She can not do these things on herself.
You're also asking your character to be a surgical technologist. They're the ones that sort through all the thousands of surgical instruments, all the sizers, the drill bits, the fiddly little strings of suture to make all the surgeon's magic even possible.
A Surgical Tech rocks the setup!
And you want your girl to all this all by herself?
Super Woman couldn't do this all by herself!
McGyver couldn't do this all by himself!
Synopsis: there is no way in hell a single person can perform spinal surgery without help. She will most likely die on the table. You do not understand how close those drills and chisels are to the aorta and vena cava. A little slip will send something sharp right into a major vessel, and then she'll bleed out. If she doesn't kill herself outright, she will faint. Like I said, spine surgery is brutality. It is physically brutal and barbaric. She won't be able to put up with the hours of agonising pain that this will cause. I'm all for acupuncture, but I don't think that's going to help much. Since she can't be asleep to perform surgery, that leaves local anasthetics. There are serious side effects (including death) if she uses too much of that.
So, what's the one caveat that will allow her to accomplish all this?
Basically: magic. She can sit herself up against Handvavium LLC's super-advanced robot and push the start button. Let the robot do all the work and she can watch it go from the screen. That's all there is to it!
But actual autosurgery? No. Not possible.