The verbs चला आना and चला जाना exhibit a slightly irregular verb form. They consist of a perfect participle of चलना followed by a form of the verb आना or जाना. The participle and verb both inflect.
चला आना means “to come” and चला जाना means “to go”. They are, in general, equivalent to आना and जाना, respectively.
They are used in an idiom that was discussed in another note.
तुम कहां चली गई – “Where did you go?” / “Where were you off to?”
इतनी जल्दी शाम चली आई – “The evening came so quickly”
मेरे दो भाई चले आए हैं – “Two of my brothers have come”
कहीं सालों से यह रीत चली आई है – “This tradition has come after many years”