Literal answer to your quetion is a Phenom II even with a cooler to OC it its Cheap. However $1000 build you shouldn't be asking whats the cheapest CPU unless you have misspent your budget somewhere.
^ This. If you're asking this question, you've mapped out your budget wrong. Theres no reason why you shouldn't be able to get an i5 in there. While most games do not use more than 2 cores, there are a few out there, and more are starting to come out. Skyrim, Battlefield 3, Deus Ex, Shogun 2, upcoming Medal of Honor (same engine as BF3) to name a few. The i3 will indeed bottleneck at higher resolutions and detail settings.