This is quite easy, so long as the word 'greatest' is clarified: it is Beethoven's Third Symphony - the 'Eroica'.
(This fact suddenly struck me with complete conviction as I was listening to the final movement on the car radio!)
Beethoven's third is, of course, a first rate piece of music; it is extremely enjoyable even to those of only modest musical understanding; it both starts and ends well (always important!) and it is long enough to impose its greatness.
But what makes this particular piece stand above all its rivals?
Not that it is better than any other - many other pieces are its equal; not that it is my personal favourite piece of music (that would be Mozart's opera The Magic Flute), and Bach was a better composer, qua composer - but the following:
1. Beethoven was the first 'great composer' - in the modern sense of a creative and original genius who was self-consciously, titanically grappling-with and reshaping his material using the whole of his large personal resources. Before Beethoven composers were servants and craftsmen, after Beethoven they were self-consciously striving to be great - like Wagner - hence diminished by some element of pretense.
2. Within Beethoven's own life, the Third Symphony was precisely that point at which he became great, fully expressed himself - yet before he became obviously assertive of his greatness by deliberate novelties and strainings (as for example in the finale of the Ninth Symphony - rather too obviously trying to impress...).
3. The Eroica has energy, technique, fluency, invention, lyricism - in a word spontaneity: it is an explosive and sustained overflow of the power of a young but mature genius just hitting his straps and surprising even himself. That kind of thing cannot be repeated - once he had done it, he knew it could be done.
4. In the history of classical music, the Third symphony is as much of a watershed as any other piece, since it was chock-full of technical innovations and a new spirit which was widely emulated. Before the Eroica was the Classical era, and after was Romanticism.
So this is quite an easy choice - Beethoven in general and the Eroica in particular are 'the greatest' in an objective and unrepeatable sense.