The option that can be used as a one-word substitute for the given group of words "based on chance rather than on reason or a plan" is arbitrary.

• Extraordinary means very unusual or remarkable.
• Unique means being the only one of its kind.
• Ordinary means normal or usual.

Arbitrary means based on personal whim or preference, rather than on reason or system. It is often used to describe decisions that are made without any clear justification or rationale.