A Bombardier private jet came within 10ft (3.05m) of colliding with an unidentified drone.
A report to the UK Airprox Board found the GL600S aircraft, coming into London Luton Airport on 26 August, "almost hit" the drone at 4000ft.
The pilot said he saw the black, unmanned drone at about 12:07 BST.
An inspection after landing did not find any evidence of a strike, the report said.
The board said it was "unable to determine the nature of the unknown object".
It said the pilot's account "portrayed a situation where providence had played a major part in the incident and/or a definite risk of collision had existed."