Please post a new question and include the date.
A date is needed. Please see the question "What is the value of a (date) US 20 dollar bill?" for more information.
$22 to $45 depending on condition
Your bill is actually called a Federal Reserve Note, like modern $20 bills, rather than "a bank note of Chicago". Chicago is simply the Federal Reserve District location that distributed the bill. Please see the question "What is the value of a 1928 US 20 dollar Federal Reserve Note?" for more information.
The star indicates it's a note printed to replace one that was damaged during the printing process. While some "star notes" can be moderately valuable, modern $20 bills are so common that the star may add only a couple of dollars at most.
All 1928 $20 Federal Reserve Notes carried the phrase "Redeemable in Gold", although they weren't gold certificates. There were also gold certificates with that denomination but they have gold seals and lack the words Federal Reserve Note. Please see the question "What is the value of a 1928 US 20 dollar Federal Reserve Note?" for more information.
It's only worth $20 unless it's old.
The value of a 2003A one dollar star note can vary depending on its condition and rarity. In general, these notes are worth slightly more than a regular 2003A one dollar note, typically in the range of $5 to $20. Rare or unique star notes may be worth more to collectors.
The US didn't print any $20 bills dated 1920. Please check again post a new, separate question with more details.
A date is needed. Please see the question "What is the value of a (date) US 20 dollar bill?" for more information.
A star note would have a slight collector value above face value, but only if the bill is in crisp uncirculated condition. It's not old enough of a series to be worth more.
it is worth much more
$22 to $45 depending on condition
A twenty dollar bill with a star on it can be worth different amounts depending on the date. A 1914 twenty dollar bill with a star on it is worth 1000 dollars.
Your bill is actually called a Federal Reserve Note, like modern $20 bills, rather than "a bank note of Chicago". Chicago is simply the Federal Reserve District location that distributed the bill. Please see the question "What is the value of a 1928 US 20 dollar Federal Reserve Note?" for more information.
A star on a 20 dollar bill signifies that the bill is a replacement note for one that was misprinted or damaged during production. It has its own unique serial number and is considered rare and collectible among some currency enthusiasts.
The star indicates it's a note printed to replace one that was damaged during the printing process. While some "star notes" can be moderately valuable, modern $20 bills are so common that the star may add only a couple of dollars at most.
Start notes are made to replace bills that were damaged during the printing process. The new note has a different serial number from the original bill but an asterisk is added to indicate that it replaces a bill which did not circulate. Older star notes and packs with sequential numbers can be worth a significant premium. However a single modern star note would in most cases only sell for a small amount, usually a couple of dollars. above the value of a corresponding standard note.