- During DNA replication, the RNA primers laid down by primase need to be removed to allow DNA synthesis in those regions.
- DNA Polymerase I has the unique ability to remove RNA primers using its 5 --- 3' exonuclease activity and simultaneously fill the gaps with DNA nucleotides, making (C) correct.
- DNA Polymerase III is mainly responsible for synthesizing the new DNA strand but does not remove RNA primers, so (A) is incorrect.
- DNA Ligase seals the nicks between Okazaki fragments but does not remove primers, so (B) is incorrect.
- Helicase unwinds the DNA double helix but does not deal with primers, so (D) is incorrect.
Answer: \(\boxed{\text{C}}\)