Which organism is more similar to a chimpanzee-an orangutan or dog?

An orangutan is much more similar - as evidenced by the fact that BOTH the chimpanzee and the organutan are order: primates, suborder: haplorhini, family: hominidae while dogs are order: carnivora, suborder: caniformia, family: canidae.

As you can see, while they are all mammals, the divergence between the apes and the dogs starts all the way up at the "order" level of classification. Dogs are more closely related to cats and bears than they are to primates like chimpanzees and orangutans.