I've been having this problem too... DX9 version works, but no DX11.
Updated ATI drivers, didn't help. Reinstalled DirectX, reinstalled Civ5, no dice. Have gone into ini file to ensure that AA was turned off. I've questioned Steam Support, no response yet.
I'm running 64-bit Win7 on an i7-930, using a single HD5870. It's a little overclocked

, but I've turned it down and tested at stock with the same results.
Only change I made before this crash was installing the SDK, and I reckon this may have something to do with it, as it changes the config.ini somehow- can anyone who hasn't installed the SDK please post their config.ini so I can compare them?
Just to be sure we're on the same page, here's the error message Windows 7 throws at me:
Problem Event Name: APPCRASH
Application Name: CivilizationV_DX11.exe
Application Version: 1.0.0.20
Application Timestamp: 4ca37045
Fault Module Name: GameOverlayRenderer.dll
Fault Module Version: 0.94.9.25
Fault Module Timestamp: 4caa36f9
Exception Code: c0000005
Exception Offset: 0002d6e6
OS Version: 6.1.7600.2.0.0.768.3
Locale ID: 3081
Additional Information 1: 0a9e
Additional Information 2: 0a9e372d3b4ad19135b953a78882e789
Additional Information 3: 0a9e
Additional Information 4: 0a9e372d3b4ad19135b953a78882e789
I can post dxdiag if it helps, but it's looong.