May 2019:

As you will be aware the first Crossrail1 project is both delayed and over budget.  Therefore, the timing for the second Crossrail line remains uncertain, as does the likelihood of a station in Chelsea.  The Chelsea Society believes that it is unlikely to come to Chelsea; however, the TfL has not yet conclusively ruled out a station in Chelsea.

TfL’s current views on the Chelsea station and on the overall project are available on their site at:  https://crossrail2.co.uk/stations/chelsea-kings-road/.