Is this a run-on sentence?
The first car that Mr. Hickman bought is still the most precious in his collection it's a 1971 Chevrolet Chevelle.

 - yes
 - no
This is a run-on sentence. It is formed from two sentences run together, joined without punctuation.
The first car that Mr. Hickman bought is still the most precious in his collection it's a 1971 Chevrolet Chevelle.
Here is one way to fix the run-on sentence:
The first car that Mr. Hickman bought is still the most precious in his collection; it's a 1971 Chevrolet Chevelle.