Here is my build for a first time gaming system

Solution
it is a revision of your build
gaming doesnt need more than 8GB of ram
for that budget, you deserves more. you can OC this setup for 10-20% performance boost

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor ($222.00 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: ASRock Z87 Extreme4 ATX LGA1150 Motherboard ($109.99 @ Microcenter)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($74.98 @ OutletPC)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @...
it is a revision of your build
gaming doesnt need more than 8GB of ram
for that budget, you deserves more. you can OC this setup for 10-20% performance boost

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor ($222.00 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: ASRock Z87 Extreme4 ATX LGA1150 Motherboard ($109.99 @ Microcenter)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($74.98 @ OutletPC)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ OutletPC)
Video Card: Asus Radeon R9 280X 3GB Video Card ($319.99 @ B&H)
Case: Antec One ATX Mid Tower Case ($29.99 @ NCIX US)
Power Supply: Corsair CX 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ Microcenter)
Total: $906.90
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-18 01:04 EST-0500)
 
Solution

Rammy

Honorable
That seems unnecessary. I'm merely quoting the specifics for both products. Sometimes these will take into consideration things like a side panel fan, or just allow extra clearance for no real reason.

In this instance, the Hyper 212 Evo is listed as 159mm tall, the Hyper 212 Plus is 158.5mm and the Antec One officially allows 155mm of clearance.

I'm not saying there is no way it will fit, in fact it would seem very strange if it didn't given the width available, but you'd assume there would be a reason for them to list the maximum at 155mm when so many popular coolers are near to 160mm (though my inner cynic says it might be to sell more expensive cases).