With an R290 in an 850 build, 8320 or 8350 are about your only choices. Even the cheapest i5 with an R290 comes in just over $900.
Wait, getting closer:
PCPartPicker part list:
http://pcpartpicker.com/p/BgzNYJ
Price breakdown by merchant: http://pcpartpicker.com/p/BgzNYJ/by_merchant/
CPU: Intel Core i5-4440 3.1GHz Quad-Core Processor ($187.98 @ SuperBiiz)
Motherboard: ASRock H87 Pro4 ATX LGA1150 Motherboard ($99.98 @ SuperBiiz)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1866 Memory ($82.99 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($51.99 @ NCIX US)
Video Card: Asus Radeon R9 290 4GB DirectCU II Video Card ($369.99 @ Amazon)
Case: Cooler Master Elite 430 ATX Mid Tower Case ($27.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($59.99 @ NCIX US)
Total: $873.92
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-08-08 16:33 EDT-0400