I have 3 years of Active Army service, and 20 years of active Army Reserve ending in an Honorable Discharge. Can I apply for 20 year letter?

SFC Robert Bishop yes you should have received one.

I thought that that letter is generated by HRC automatically ? I'd get with S-1 .

I think Your last 3 year’s Must be in the Selected Reserve prior to applying for twenty year letter. Check the regulation as you can google or call HRC retirements

You should already have received one when You hit the 20 year mark.

The 20-year letter is generated automatically, but there are any one of a number of reasons that you didn't get at the time, the most likely being that you did not have an updated home address in the system.
To apply for a letter, check out the link below (bottom most section).
https://www.hrc.army.mil/content/Notification%20of%20Eligibility%20for%20Retired%20Pay%20At%20Age%2060%20%20%20%20%2020%20Year%20Letter

You should have received a letter of eligibility already since you have 23 years TIS. I would hit the S1 up and have them get you that document. While I was waiting, I would sit down with the S1 and have them pull all your retirement point records and go over them and see if you agree. I will point out that the National Guard System and Army Reserve System didn't use to communicate, so you may have to get any of those records from NGB or your old state command if you did any guard time. You won't be able to actually retire until you approach age 60, so to maintain your "Gray Area" benefits, you need to request transfer to the Retired Reserve. Then about 9 months before you are eligible to retire, you need to contact HRC and initiate the paper work. They no longer mail the applications to you when you approach eligibility. There are some early retirement rules available now that were not there when I was still active reserve, you might want to check on them since you have 3 active years.