Currently chains can be triggered by several events: deliveries, manual invocation, or by a schedule. Other events being worked on include being invoked by another chain, or by a REST services.
However, currently, stage promotion (of an item? or project/stream? or baseline?) which doesn't involve a file content or file/folder name change, is not an event that Pulse responds to.

I guess to consider this as an enhancement, we'd be interested in the use case. Promoting doesn't change the file content of the stream, so the working location populated by PulseUno would remain the same as before the promotion. However, if you were using the Deployment areas their content may change - but PulseUno itself doesn't really use these. By understanding what you're trying to achieve we may be able to come up with a possible solution using existing features, or come up with a potential change that is even more useful to all customers.