There's a combination of reactions going on when aqua regia dissolves gold. Aqua regia combines the presence of a strong oxidizer (nitric acid) and the free chloride ions (from HCl) which readily dissolves gold. Other strong oxidizers are also formed in the mixture, most notably chlorine gas and nitrosyl chloride. However, the main reaction is the oxidation of gold by nitric acid and the subsequent stabilization of the gold ion by chloride ions.
1): Au(s) + 3NO3-(aq) + 8H+(aq) <=> Au3+(aq) + 3NO2(g) + 3H2O(l)
1 is an equillibrium reaction, and under normal conditions the equillibrium is favored towards the left side. So as soon as an Au+3 ion forms, it goes back to form solid gold. As a result, you don't see any reaction. However, if you can remove the Au+3 ion from solution, the reaction then moves in the forward direction. This is where the free chloride ions come into play.
2): Au3+(aq) + 4Cl-(aq) -> AuCl4-(aq)
Reaction number two removes the Au3+ ion from solution thus causing the equillibrium of reaction number one to shift over to the right causing solid gold to be dissolved. For reaction number one, you can use pretty much any strong oxidizing agent. In fact, in the real reaction it generally is more than just the nitrate ion doing the work as other oxidizers which form help create Au3+ ions.