Yes, this structure is possible.
The main reason this is possible is because of resonance. If you look at the alternative resonance structure, there would be a double bond connected to the oxygen and a single bond connected to the nitrogen. The problem with this structure however is that there would be a positive charge on oxygen and a negative charge on oxygen. This wouldn't be the best structure to draw because oxygen is more electronegative than oxygen, and therefore should have the negative charge.
It's best to think of the octet rule as a guideline rather than a law. While yes, it is best to give atoms a full octet and to reduce formal charges, there are still exceptions, such as this structure.