The enzyme that cuts DNA at specific places is known as a restriction endonuclease. Among the options provided, the one that fits this description is :

Option C : E.coli restriction endonuclease I

Restriction endonucleases, also known as restriction enzymes, are enzymes that cut DNA at or near specific recognition nucleotide sequences known as restriction sites. E.coli restriction endonuclease I is an example of such an enzyme, derived from the bacterium Escherichia coli (E. coli). These enzymes are essential tools in molecular biology, particularly in processes like gene cloning, as they allow for precise cutting and manipulation of DNA.