The gold is in the red chest.
IF the gold is in the green chest, then all three statements are true, a contradiction. So the gold must not be in the green chest.
Statements 1 and 2 are equivalent, so they are either both true or both false. If both Statements 1 and 2 are true, then Statement 3 is false. If both Statements 1 and 2 are false, then all 3 statements are false.
Therefore, Statements 1 and 2 must be true while Statement 3 must be false, i.e. the gold must be in the red chest.