The (other/another) day I saw Chuck Norris fighting in the park.

The correct phrasing would be: "The other day I saw Chuck Norris fighting in the park."

"Another" is typically used when referring to an additional item of the same kind, while "the other" is used to refer to a specific instance that is distinct from the current context. In this case, "the other day" refers to a specific, previously mentioned time.