In order to have a bright chrome finish that is suitable for outdoor exposure the plastic part would have to be produced in a chrome plating grade material.
This is generally a plating grade of abs but other polymers can be used.
Typical applications are automotive exterior badges, nameplates, trim and handles. Spa, pool and plumbing fixtures are also good examples.
This process is available from only a few suppliers specializing in plating on plastic. The industry is highly regulated and requires a large capital investment.