The pH is determined using the formula:
\[\text{pH} = -\log_{10} [\text{H}^+]\]With a hydrogen ion concentration of \([\text{H}^+] = 10^{-3} \, \text{M}\), the pH is calculated as:
\[\text{pH} = -\log_{10} (10^{-3}) = -(-3) = 3\]Therefore, option (1) is the correct answer.