You’ll want to address your hips.
The muscles in your hip may not be firing correctly or your pelvis may be out of line.
If one hip is dropped when running it could indicate weak hip abductors and external rotators.
You may be seeing compensation for what is missing/restricted on the opposite side.
How you sit or stand could be an impacting factor.
Why Sitting Wrecks Your Mad Hip Action
Episode 88: Desk Athlete Hip Rescue
Episode 276: MobilityWod Google Talk: Desk Bound

Episode 251: High Skilled Sitting/Abdominal Bracing

Episode 14: Celebrity Goat Death Match: Chris Spealer
Foot Position Test: Breaking Diane
Episode 166: Ninja Recovery and Some Shoulder & Hip Love
Episode 13: It’s Just Movement, Break it Down
Episode 241: Sumo and Medial Chain Business