Chrome-moly is a type of steel, such as "Chrome-moly 4140", a typical gun barrel steel. This is steel which has chromium and molybdenum.
In addition, mil-spec barrels, since the M16A1 during the Vietnam War, have their bores and chambers chrome plated, or "chrome lined". Only the bore and chamber, not the outside. This is for resistance to corrosion in humid jungle environments. And while it does make cleaning the bore and chamber easier, according to at least a few manufacturers, it detracts from accuracy. (This is highly debate on this board.)
Then there are stainless steel barrels. Usual material is 416F stainless. This steel is excellent for barrels, and according to my machinist friends, is more similar to chrome-moly than it is to a true stainless steel. This material, naturally, would not require chrome lining of the bore and chamber, as the material itself is resistant to corrosion. This is a favorite material for match barrel makers. Some shooters do not want a shiny barrel reflecting light. Stainless barrels can be had with black oxide coatings, or can be black tefloned.
It is said that stainless is not good for sustained high rates of fire, as it retains heat more than chrome-moly. I have three rifles with 416F stainless. The heat issue is a non-issue, at least to me, firing only semi-auto. Perhaps for a full-auto military or LEO rifle that may be a different story.
I have both stainless and chrome-moly barrels in my assortment of rifles, but wish they were all stainless. If I lived in a drier climate, chrome-moly would be just fine, I am sure. I personally would not pay a premium for a chrome-lined barrel. That is my opinion, others on this board will give you differing advise.
(Edited to correct spelling of "molybdenum". Duh.)