To find out how many chicken wings Curt ate, we first determine Dwayne's eating rate. Dwayne ate 45 chicken wings in 5 minutes, which means:
\[ \text{Rate} = \frac{45 \text{ wings}}{5 \text{ minutes}} = 9 \text{ wings per minute} \]
Since Curt ate at the same rate for 3 minutes, we can calculate how many wings he ate:
\[ \text{Wings eaten by Curt} = \text{Rate} \times \text{Time} = 9 \text{ wings per minute} \times 3 \text{ minutes} = 27 \text{ wings} \]
Therefore, the total number of chicken wings Curt ate is \( \boxed{27} \).