The Combine-Chimera Alliance was a secret alliance made between the Empire of the Combine Race and the Chimera somepoint before the First War, it was revealed to the Multiverse on The Day the Multiverse Burned when it betrayed the Axis of Empires and became the main faction that the Alliance fought against until 2364 N.E when it effective dissolved following the destruction and (temporary) extinction of the Chimera.
It's largely unknown when the Combine-Chimeran Alliance came to be, but many theorize that the Combine-Chimeran Alliance came to be due to the actions of Emperor Yiloala Kutarukia in some shape and form, either through manipulations or clever wordplays, whatever the reason, the Empire of the Combine Race and the Chimeran Empire forged a secret military alliance that would conquer most of the known Multiverse on and most of the years after The Day the Multiverse Burned. It appeared as if the Combine-Chimeran Alliance would win the war, but the Third Human Republic intervene just in time to prevent the Alliance from finally being conquered by this brutal alliance. Some say the aftermath of the Third Human Civil War is what lead to Emperor Yiloala to reveal the secret alliance between the two powerful empires, knowing that the Third Human Republic would eventually lead to his defeat and tried to prevent this by simply accelerate his plans and conquer the rest of the Multiverse before the Third Republic has a chance to mobilize. Unfortunately for him, and fortunately for the rest of the Multiverse, he didn't exactly expect the Alliance nor the Coalition (even if, by that point, they were forced out of the war entirely and simply consolidating their holdings) to hold out for so long that the Third Republic finally became involved in the First War entirely, which lead to this Alliance's destruction and the slow and brutal campaign into the Combine Homeworlds and Colonies, as well as the eventual end of the First War entirely.
While not unified in the slightest way, with both Empires still fully independent of each other, they did, however, followed the orders of either Emperor Yiloala or the Monarch of the Chimera and other heads of both Combine and Chimeran Governments, making the Combine-Chimeran Alliance's sort of speak government akin to an form of Oligarchy with fascist and otherwise totalitarian tones to it overall
while both fully independent of each other, they still worked together in a brutal and effective campaigns that showed the known Multiverse as a whole that throughout the entire war, the Combines and Chimera were simply holding out of their true military might in utterly horrific ways. This reason alone is perhaps the biggest factors that would have lead to the Combine and Chimera to nearly completely conquer the Multiverse as a whole if it wasn't for the Third Human Republic's almost timely intervention that finally tipped the scales in the Multiverse's favor.