Answer:
'The First Spacecraft to take close-up images of an Asteroid was Galileo'. The name of the Asteroid is '951 Gaspra' or just 'Gaspra'. It took up images of the Asteroid when it flew past Gaspra on 29 October 1991.
Article : Advances in Space Science
Next Question: Who discovered 'The Asteroid - Gaspra'?
Previous Question: What is the number of Variable Stars in our Galaxy?