A reasonable Lewis structure is #H-O-stackrel(+)N(=O)O^-#. One of the oxygen atoms has a formal negative charge, and the nitrogen atom is quaternized and bears a formal positive charge. Of course, the molecule is neutral, and the Lewis structure reflects this.
Note that when nitric acid dissociates:
#HNO_3(aq) + H_2O(l) rarr H_3O^+ + NO_3^-#
There are 3 formal charges on the nitrate ion: #""^(-)O-stackrel(+)N(=O)-O^-#. The overall charge on the ion is still #-1#, but there is again formal charge separation in our representation of the anion.