Will a ddr3 1066 RAM work in a ddr3 1800 slot?

The slot itself is categorized as "DDR3" so it will fit.

The speed of the RAM will only work if your motherboard supports that speed. Therefore, check your motherboard manual to determine if it supports DDR3-1066 RAM.

If you mix up your RAM with different speeds, such as using a DDR3-1066 with a DDR3-1800, then the RAM speed will be matched with the lowest speed, making both RAM operate as a DDR3-1066. Mixing RAM of different speeds isn't recommended.