Chemosh seem to be the god of the Moabites. Moloch was the god of the Amonites. Do they worship only one God too, like Israel?
It was common for cities in that area in that time to have their own "City-God" who took care of the city. They acknowledged the other gods of other cities as legitimate gods, but they weren't "their" god and if you worshiped someone else god then you would make your god angry. Additionally the wars between the gods were a reflection of the on-going enimosity between the cities themselves.
The degree to which they worshiped only the main City-God varied a lot, sometimes they also worshiped his wife, his children, his brother, a whole pantheon.
A stele was found in the area of ancient Moab from the 12th century B.C. during Pharaoh Rameses II's domination of Canaan, which depicts a local ruler flanked by two (possibly Egyptian) gods, and the stele is made in imitation of the Egyptian style.
Eveline J. van der Steen in her book "Tribes and Territories in Transition" pg. 303 writes:
On the Biblical Archaeology Society's page for the Balu'a Stele they write:
So the Egyptianization of the region may have contributed to early Moab's religion and pantheon.
Archaeologist Gabriel Barkay in the article "What's an Egyptian Temple Doing in Jerusalem?" (Biblical Archaeology Review Vol 26 No 3 May-June 2000), wrote about the presence of an Egyptian Temple in Jerusalem during the Canaanite/Jebusite occupation of the city, before the Israelites conquered it and supplanted it with monotheistic worship of Yahweh in Solomon's Temple. Noting a number of artifacts present he mentions some pottery dating to the 18th dynasty of Egypt:
Then he also notes a religious statuette found as well:
This is additional corroboratory evidence that the Egyptians successfully introduced their religion to their Canaanite vassals, and the Balu'a Stele is most likely evidence of that in Moab as well.
As for additional reading on Chemosh, in a discussion I had with the Hebrew scholar Gershon Galil about a Moabite seal of a ruler bearing a theophoric element of Chemosh's name, through his Facebook page (possibly viewable to the public here), he told me: "For Chemosh see Müller, Hans-Peter. "Chemosh." Dictionary of deities and demons in the Bible. Edited by Karel van der Toorn, Bob Becking, and Pieter W. van der Horst. 2nd ed. Leiden: Brill, 1999, 186-189." I hope that helps.