How much would it take to retrain a lv4 paladin into a chosen one paladin?
To gain an archetype that replaces standard class abilities you already have, you must spend 5 days for every alternate class feature you would add, subtract, or replace by taking that archetype. At the end of the training period, you lose the standard class features and replace them with the archetype's alternate class features (if any).
At level 4,
you would replace Lay on Hands, Channel Positive Energy, Divine Grace and Smite Evil for two class features.And you lose your Divine Bond feature, while gaining Divine Emissary and Religious Mentor.
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Now, the rules say "or" instead of "and", so I guess you can choose whatever benefits you most.
I would say that you need to "add, subtract, or replace" 5 class features if you want to gain the Chosen One archetype at level 4, so that would take you 25 days.
The cost for retraining is days x level x 10, so that would cost you 1000gp.