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Then yes (theoretically, but not practically). For a rigid body, which the swing can be treated as, to maintain a static system three static conditions must be met. We'll use these 1) ΣFx=0 2) ΣFy=0 2)ΣM=0, where these equations means that the sum of forces in the x and y directions must be balanced, and the third signifies that the sum of moments (torques) about some axis (we'll use the junction of the swing and connected chain, but it must hold true for any arbitrarily selected point) must be balanced. In your case, the sum of forces will be balanced, since the only forces are in the y direction, your weight and the reaction force from the chain. However, there is a moment about the swing-chain junction caused by your standing on the swing that is unopposed. Therefore Eq(3) cannot be true. However if you hold onto the chain, you could in principle, if you were really strong, completely balance your own weight so that the moment about the junction vanishes. Then your arm on the free chain is supporting only the weight of the swing itself, which can be treated as a separate system, since your weight is no longer applied to it (or negligibly so). In short, if you're a strong as an Olympic gymnast, then probably its possible.