Here's my analysis --

First, a bit of history: California card rooms used to be smaller places dealing draw games (lo-ball and jacks-or-better) only, because of state law. Card rooms in the Los Angeles area were all located in Gardena, and limited to max of 35 tables each. The California state law didn't permit games of chance and something called "stud-horse poker". After a bunch of litigation, it was decided that stud & hold'em games were games of skill, permitting expansion of these more popular games statewide (this was in the late 70's). The first LA area city, outside Gardena, to offer poker games was the Bicycle Club in Bell Gardens, an industrial small city. The tax revenue on expanded poker games was attractive, so "The Bike" was built and opened to large crowds. Not long after, City of Commerce allowed poker in their town, and so the California Commerce Casino was born in 1980. It opened with about 40-50 tables (I could be off on # of tables), and I was there within the first week to pick up chips from this first issue series, the HHR mold (Langworthy) series.

My point in covering the history is that Commerce was never a small 4-table back-room card club in rural California. It opened with a brand new building, significant investment and professional Las Vegas quality chips from the start.

California Commerce Club chips (spelled out):
If you look at the Staeffler section on California Card Clubs (pg. C-7), you will see a page full of mostly cash-value chips, all in either the HHR mold or H&C mold. The HHR chips were first, and note that they used center inlays even on the fractional chips. As they expanded, they switched to H&C chips, and hot stamped the lower denominations (up to $2) and used inlays on higher denominations. A typical order pattern for cost-minded casino management. In all cases, they used at least the casino's full name on value checks, and used additional identifiers (logos, location, etc.) and anti-counterfeit protections (molds, inserts, etc.) on their chips. See screen capture of pg. C-7 below. [Note: the green "BJ8" mold chip on the page is misplaced -- it is a Normandie Casino, Gardena chip.]

CCC chips (with initials):
The Steffler section on California Card Clubs (pg. C-27) shows some "CCC" chips attributed to Calfornia Commerce Club. A group of 3 H&C hot stamps, a group of 2 HHR hot stamps and a group of 3 plain-mold chips, hot stamped with denominations of $1, $10 and $20 and noting "scan needed". (The next page also shows a couple more "CCC" chips too.) The H&C and HHR molds are consistent with value checks used, see pg.C-7. These hot stamped chips have no other identification, but are NON-VALUE chips. As such, they may have been used for some non-gaming purpose (rack dividers, etc.) though I don't have direct knowledge of these chips. Screen capture of this page is below --

The $1 "CCC" plain mold chip:
In contrast, the value chips are a plain mold, not used elsewhere at the California Commerce Club. Furthermore, the "CCC" hot stamp looks like a diamond-shaped generic monogram. Certainly not the rounded "C's" used elsewhere by the CCC. The monogrammed "CCC" is still a special die, which needed to be created, so why would management pay for a die that looks nothing like their logo? The obverse only has the "CCC" monogram, no other city/state, etc. as protection from similar counterfeit chips being cashed. Yes, $1 is a small denomination, but the page listing also shows a $10 and $20 denomination of the same style. Can you imagine a $20 VALUE chip with such little protection being ordered by a large, professional club in the 1980's??? I can't. On the reverse side is the denomination (only). All the other known California Commerce Club chips use a simpler denomination format , that is $1 NOT $1oo. The expression of the underlined double-zero is from an era earlier than the 1980's (though there could be a few exceptions).

I've added your scans of the $1 chip in question below, just so folks don't have to go to your original post to view it --

My conclusions:
I don't know where the chip is from, but I'd bet heavily against the California Commerce Club. It may be a home game chip or perhaps a small club or illegal chip. It may remain a UFC forever. But unless someone steps up and says that the personally procured this chip from the California Commerce Club, I'm a skeptic. In the early days of the hobby, before we had some of the records we now have, it wasn't unusual for initials chips (i.e. CCC, LVC, etc.) to be "reverse-engineered" into attribution from a known club/casino, especially if Nevada attribution was being touted. Some speculation was to improve the price/appeal of a UFC chip, but much of it was our (the hobby's) desire to solve the puzzle of UFC chips. Some attributions are confirmed, while others are rejected later on. It's just part of the hobby.