Maybe use some vertically-oriented pieces of 2" aluminum angle-iron to distribute/carry the load at the corners.

I tried and tried to attach photos of a stucco mounted antenna
I recently installed but I keep getting a message that I'm over
the 500 mb limit. In any event, I would suggest you go into your attic
and survey the inside of the stucco chimney. You probably have 2x4's
at the four corners. If you cut another 2x4 about 2-3 feet long and
put it on the inside of the chimney, you can use a "Y" style mount.
One side of the mount will go into the corner 2x4's and the other side
of the mount will screw into the 2x4 you placed behind the stucco
in the attic. Hope this makes sense. Grounding the mast and cable,
while not perfect is certainly better than nothing at all.

Interesting. Did you fasten the 2x4 ahead of time, or let the bolts/screws from the Y bracket suspend it from the outside?

Actually, I did the following:
I cut a 3 foot long 2x4 and drilled two large holes in it about
two feet apart for the two "Y" brackets.
I brought the 2x4 and a drill to the chimney and using the
two pre-drilled holes, placed the 2x4 against the stucco and drilled
through it. I purchased two 6 inch long lag bolts with washers and
screws. I put a washer and lag bolt through the 2x4 and taped the
heads securely to the 2x4. I brought the 2x4 into the attic and
aligned the lag bolts to the pre-drilled holes in the stucco. I then
pushed the lag bolts/2x4 through the holes. The lag bolts were
long enough to hold the 2x4 until I could get to the roof.
Once on the roof, I attached a large washer, "Y" bracket, another
washer and NUT. I attached the other side of both "Y" brackets
to the corner studs using wood lag screws with washers.
Because it can get windy here, I supplemented the install with
a U-bolt on the mast and two steel "arms" fastened to the top
of the chimney. Those arms are fastened into the studs inside
the attic.

@JoeAZ, I think you meant:
"Once on the roof, I attached a large washer, "Y" bracket, another
washer and [NUT]."

I read it several times confused until I made that assumption...

Many years ago I used some 6 inch lengths of 1/16" thick pieces of 1-1/2" aluminum angle on the corners of of a stucco chimney and it worked fine. You can find it in your local big box home improvement store. A four foot section will give you eight 6 inch pieces.

A Couple Mast Questions....

Standard CM masts are 5' and 18-gauge 1.25" diameter tubing. Seems WAY too weak.
I was thinking of galvanized pipe available at my local Home Depot. They have 10' lengths of 1" and 1.25" which are much thicker than 18 gauge. They also have thicker and bigger fence posts. My calculations show that if I apply a 10 lbs load to the end of a 5 foot tube:

1-1/4" 18 ga. displaces 1.21"
1" galv pipe displaces 0.25"
1-1/4" galv pipe displaces 0.10"
1-7/8" 16ga displaces 0.17" (fence post)

I can't imagine using the 18 ga spaghetti noodle, do people use those? What do you guys recommend? Would anyone put the antenna on a 10' mast (1.25" galv pipe) attached to the chimney? Would I even need that? I mean if 5' mast on my roof doesn't work, will 10' really matter? Fence post comes as 8' might be a good option?

Next.....

If I secure a mast solidly to the chimney, and find the "best" orientation and tighten the CM-3020 (arrives today) to the mast tightly, will wind or anything else change my "lock"? I'm assuming that I'm NOT going to have to continuously adjust things up on my roof, but I have zero experience with an antenna and wind!

A 5' difference in height can sometimes mean all the difference in the world between a poor signal and a good signal. Every installation is different.

My mast material of choice is 1-1/4" galvanized steel electrical conduit. It has an outside diameter of 1-1/2" and comes in 10' lengths.

It is possible for an antenna to shift in direction in a really bad storm, but if everything is securely tightened I have found them to be trouble free.

Tim, thanks for your reply. I'm honestly surprised that EMT is acceptable since it's "bendable" by design and is only 0.065" thick! It's certainly affordable though....

The conduit is about 33% thicker than the 18 gauge steel used in the TV masts...and the TV mast is certainly acceptable for most applications...I have a small VHF ham radio antenna mounted on top of two 10 ft sections of TV mast and have never had any issues with it. I have also seen many TV antennas mounted on a 21 ft length of 1-3/8" chain link fence top rail. Most of it is commonly 17 gauge steel.

I suspect that your choice is the correct one....
Upon further analysis using this online deflection calculator:
https://www.engineering.com/calculators/beams.htm

Your recommended EMT bends 0.19" at 5 ft with 10 lbs. At home Depot a 10' length costs $18.50. Weight is 11 lbs.

1-1/4" galvanized pipe (0.14" thickness) bends 0.12" at 5 ft with 10 lbs. At home Depot a 10' length costs $38.87. Weight is 22 lbs.

The stiffer pipe isn't justified IMO confirming your choice. Thanks again for your information.

Well, thanks for all the help on this thread folks!
Unfortunately, I didn't get very good news this weekend. I first assembled my CM-3020 (Advantage 100) in my second story bedroom and pointed out the window towards the Mt. Wilson towers that broadcast LA signals. I hooked it up to a small TV I've got and got ZERO channels. That was quite depressing. I then disassembled it and reassembled it outside, mounted it to a 10' mast and held it on to of an 8' ladder. That was a funny looking scene, I'm sure. I tried pointing it in various Eastward directions and was able to tune from 12 to 25 digital channel this way, but they were very very poor reception, and mostly black or solid pictures. I did get a soccer game and Telemundo or something else I wasn't interested in, after being on the ladder for about 45 minutes we called it. I know that things would improve with additional height, but I was aiming towards a fairly clear/unobstructed view of the mountain ranges between myself and the tower. But after seeing the size of this advantage 100 (I knew it was big, but WOW), knowing it was going to be another 5' to 10' above the chimney, the wife politely said "enough". So, I'm having to admit defeat here guys. Thanks for all the advice, I really appreciate your inputs. It's really a shame my location is so challenging, because I was ready to cut the cable...it just wasn't in the cards this time. Good luck to others who read this thread with similar aspirations, I sure hope you have better results than me!

Question: When you tried the antenna from the second story window did you open the window and remove the screen (if it was metal)? Some windows and window screens block TV signals. That you got some stations from about 10' in the back yard and inside the house suggests something was blocking the signal.