It’s better to leave olive oil stored in a cool, dark place outside the fridge. Olive oil will form crystals and start to solidify when subjected to cold temperatures. Once the olive oil is brought back to room temperature, it will return to its liquid state. Some research suggests that repeated thawing and cooling – such as storing it in the fridge between uses – puts stress on the oil and can result in condensation inside the bottle that will negatively impact the quality of the oil and its shelf life. It’s also inconvenient to bring the olive oil back to room temperature to use it.
It's also worth noting that some people believe you can use the refrigerator to test the authenticity of extra virgin olive oil. This is simply not true. Extra virgin olive oil will crystallize and/or solidify at a wide variety of time and temperature exposures. All this variance is part of what makes extra virgin olive oil truly special. So, forget the fridge, and focus instead on enjoying the wide variety of flavors found among extra virgin olive oils.