There are many reasons dealing with shear size, complexity, and cost. Example: A single US F-1 engine from the Saturn V moon rocket, with one very large nozzle directing 1.5 million pounds of thrust, was a very complex and costly nozzle design to build. The fabrication tooling and vacuum braze chambers needed for it were tremendously large and costly. On the other hand, the Russian RD-170 engine, with 4 smaller thrust chambers directing a total of 1.9 million pounds of thrust, was able to take advantage of a thrust chamber technology that had already been proven using very similar sized tooling and similar fabrication methods used for other Russian engines. It's basically a tradeoff. The single thrust chamber engine has fewer parts and is theoretically more reliable, but more costly and complex to build. The multiple thrust chamber engine has more parts and a theoretically higher probability for more things to fail, but is much less costly and complex to build.
In general, the Russian engine manufacturers have taken an incremental approach to their rocket engine improvements over the years. They typically make evolutionary improvements to existing designs and have produced a very large number of different engine designs over the last 40-50 years, all building on similar technology. The number of US engine designs have been far fewer and have typically been "clean sheet of paper" designs rather than improvements over older designs, with some exceptions. The differences in the systems of government between the US and Russia (USSR) have also had a significant impact on the technology philosophies their respective space programs have taken.
Incidentally, there are at least a couple US engines, Rocketdyne's MA-5 and Aerojet's LR-87, which incorporated multiple thrust chamber assemblies. The RD-180 engine (using 2 thrust chambers) is a derivative of the Russian RD-170 engine and is being used for the US Atlas 3 and 5 launch vehicles.
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