To find the fourth term of the sequence 64, 16, 4, ..., we first determine the common ratio.

The common ratio \( r \) can be calculated by dividing the second term by the first term:

\[
r = \frac{16}{64} = \frac{1}{4}
\]

This is a geometric sequence with the first term \( a = 64 \) and the common ratio \( r = \frac{1}{4} \).

The \( n \)th term of a geometric sequence is given by:

\[
a_n = a \cdot r^{(n-1)}
\]

For the fourth term (\( n = 4 \)):

\[
a_4 = 64 \cdot \left(\frac{1}{4}\right)^{(4-1)} = 64 \cdot \left(\frac{1}{4}\right)^3 = 64 \cdot \frac{1}{64} = 1
\]

So, the fourth term is 1.

The correct answer is A. 1.