When it starts moving, a bell goes 'ching-ching.' That's why it's called a ching-ching train.
Literal
Moving-out time, bell [subject-が] 'ching-ching' [quotative-と] rings. Therefore, ching-ching train.
ちんちん is the mimetic for a small bell's ring. ちんちん電車 ('ching-ching train') is the colloquial name for a streetcar/tram — named for the bell sound the conductor rings when departing. だから ('therefore') draws the etymology. The sentence is a self-contained etymology lesson about a beloved Japanese word.