Ok I solved it. Now the title of the thread can match the content of the thread.
First some proof that I solved it and little smiley icon:
chimerasolve1.jpg [ 63.07 KiB | Viewed 481 times ]
chimerasolve2.jpg [ 68.08 KiB | Viewed 481 times ]
Ok here are the steps.
1) Solve the 2x2 blocks around each corner just as you would the 444AI. I won't give instructions for that but will once again thank rline for his tutorial
which is excellent. No need to do what he calls "Step 5" in that video series. Just solve the four blocks.
2) Pair the remaining edges with the center pieces so that you get to this stage:
chimerasolve6.jpg [ 79.58 KiB | Viewed 481 times ]
3) The image above is a reduced 444AI. Solve it again.
4) You get to this stage:
chimerasolve3.jpg [ 76.62 KiB | Viewed 481 times ]
5) Solve it as a 2x2.
chimerasolve7.jpg [ 74.36 KiB | Viewed 481 times ]
OK the way you do step 2 above, which is the key step, is to pair up the edges like in the diagram. Orient the blocks using whatever method you use to rotate the 3x3 blocks cw or ccw and perform U' to match the blue with the blue. Then rotate the block cw, putting the newly formed pair into the bottom row (of the top half of the puzzle). Put it off to the side with Uu or U'u' (being careful not to rotate a reduced edge into the block because it will get wrecked. so pick Uu or U'u' to make sure you wreck something), then rotate ccw the block that you had to rotate cw and perform U to fix the 444AI stage. Repeat that for the 24 pairs.
Alternate method is to intentionally reduce the 3 edges that belong on a single 3x3x3 block and once you have the three reduced, solve the block using your usual 444AI method. I found the above method easier.
What you don't want to do is reduce it this way, which is what I was attempting to do above:
chimerasolve4.jpg [ 77.09 KiB | Viewed 481 times ]
The "Wrong reduce" image is the result of many years of habit of reducing centers and pairing edges when solving the 6x6x6 and other higher ordered cubes. I'm not surprised that my first efforts were to reduce the Chimera 2x2+6x6 this way, but really you have to do it the other way.
I don't have an 8x8x8 to test it on, but I'm pretty sure this method would work for the next higher ordered chimera (and all other higher ordered chimeras), except you would have to solve the 444AI, then reduce, then solve the 666AI, then reduce, then solve the 888AI.
Much thanks to Mr. Burgo for his tip!
Also I believe I have met SuperAntonioVivaldi's challenge
to solve a 6x6x6 without facing parity. I haven't actually tried it on an untaped 6x6x6 but one should be able to use this method.