Given that $a, b$ and $c$ are non-negative integers, i.e., $a,b,c\geq0$
and $\log a + \log b + \log c = 0$
$\implies\log abc=0$
$\implies abc={10}^{0}$
$\implies abc=1$
Since $a,b,c$ are non-negative integers, $a=b=c=1$
$\implies a+b+c=1+1+1=3$
So, (A) is the correct answer.