Open
My middle ages started out peacefully enough, beginning in 730 BC. Due to a research SNAFU, I didn't pick up Monarchy until I traded feudalism for it. I decided to wait until I had completed my anarchy (5 turns) before invading the Aztecs. The Incan nation became a monarchy in 290 BC.
The Aztec war: Immediately after becoming a monarchy, I declared war on the Aztecs. It was slow going at first with only swords slogging through the mountains and marshes. In 190 BC, I captured Tenochtitlan. They had finished the Pyramids only 2 turns before, and my growth took off like a rocket from that point on. In 130 AD, we signed peace with the Aztecs, leaving them with only 1 city. Two turns later in 150 AD my workers completed the road bringing horses into my empire. The age of the knight is here! (I should note that since I discovered chivalry and hooked up horses at virtually the same time I never produced a single horseman.)
The Celtic War: As the war with the Aztecs wound down, I was trying to decide who to attack next. When I got a message that the Celts had completed the Temple of Artemis in Entremont, my decision was made for me.
The war was slow going at first, since no knights had reached the frontier yet. War with the Celts is declared in 330 AD. The first swordsman to attack in the war scores a Great Leader and an army of MI is born. In 430, the MI army takes Entremont, capturing the ToA. Unfortunately, I can't get supporting troops there fast enough and two turns later it deposes me and takes my army with it.

It takes a few turns, but the oncoming wave of knights, spearheaded by a shiny new knight army retakes the city and slowly grinds the Celts under their hooves. I also managed to get my Golden Age in 530 AD on about the 7th try with a Chasquai Scout. The last Celt city was taken in 690 AD and I turned my sights to the Western end of the continent.
The war that wasn't: In 630 AD, a Carthagenian warrior was wandering by my knight army as it was mopping up the last of the Celts and decided to attack. He was the only ground invasion force I saw from them for the rest of the game. I payed the Japanese 250g for an alliance, captured the one Carthagenian city near my empire, and ignored them for the rest of the game. It was fun watching the Samurai raze Carthagenian cities though.
In 660 AD, I redeclared on the Aztecs, finishing the remainder of their empire in only 4 turns.
In 680 AD, I finished researching Military Tradition and turned research off for the rest of the game. I also set my lux slider to 100%. I finished Sun Tsu's in 700 and all of my knights were upgraded to cavalry.
The Greco-Indian-Roman War: For the sake of speed, I decided to open a 2nd front to attack the Greeks, sending forces West into Greece that would eventually meet my Northern forces attacking through India and Rome. In 710 AD, I declared war on Greece and India with my freshly upgraded cavalry and 2 knight armies leading the charge. The Indians went down quickly, but the Greeks put up some spirited resistance around Athens and it took about 4 turns for my cav to take it. Once India was destroyed, my northern forces invaded Rome while the Southern ones carved up the remaining Greek cities. The 2 forces linked up along the Greco-Roman border. Two more GL's were spawned during this time, producing 2 cavalry armies.
In 860 AD, only 2 Roman cities remained and their half-dozen or so defenders were facing 80 or so cavalry and 4 armies closing in on them. I reached the domination limit on that turn, just as Mapstat/Civassist suggeted.
Final Results:
Entry class: open
Game status: Domination Victory for Inca
Game date: 860 AD
Firaxis score: 4916
Jason score: 9984
Time played: 33:00:58
This being my first COTM, I'm pleased with the results, and just by the fact I won the game (I think this month's GOTM at Emperor level might not turn out so well.) I found the hardest thing to do (for me) was to start my GA. My strategy was to rush a Chasquai Scout near the front lines and have it attack a wounded archer/horseman/warrior. It took about 7 tries to win a battle even with this strategy.

I think the RNG was a little nicer to me on other things though. I produced 5 MGL's and popped 4 GH's (only 1 tech though, and some nice maps.)
All in all a fun game and I'm looking forward to the next one.