Brandon Marshall -- Cleared for Takeoff ... After Punctured Lung Injury

Chicago Bears fans can take a deep breath, 'cause Brandon Marshall's punctured lung is doing MUCH better ... so say his doctors who allowed the WR to begin flying again ... TMZ Sports has learned.

We broke the story ... Marshall had to miss a court-ordered deposition last month stemming from a case in which he's accused of attacking a woman outside of a NYC nightclub in 2012.

Marshall claimed doctors told him it was unsafe to fly since he had just suffered a punctured lung from a hit he took during a Thursday Night Football game.

But everything's been healing well ... and earlier this month, Marshall told the court he's been cleared for takeoff ... and was willing and able to attend a makeup depo on January 30th.

Sources tell us Marshall made his appointment and sat for a deposition without a hitch ... or a breathing issue.