Step 1: Understanding the Concept:
Chronological arrangement requires identifying the specific historical dates for each milestone in the evolution of European integration.
Step 2: Detailed Explanation:
Determining the years for each event:
- Establishment of EEC (2): The European Economic Community was established in 1957 by the Treaty of Rome.
- Signing of Maastricht Treaty (3): This treaty, which formally created the European Union, was signed in 1992.
- Introduction of Euro Currency (1): The Euro was launched as an accounting currency in 1999 and entered physical circulation in 2002.
- Britain's Exit (Brexit) Referendum (4): The United Kingdom held the referendum to leave the EU in June 2016.
Step 3: Final Answer:
Arranging these chronologically gives the order: 1957 $\to$ 1992 $\to$ 1999 $\to$ 2016.
This sequence corresponds to the numbers 2, 3, 1, 4.
Therefore, option (A) is the correct answer.