Is the serial number JS2102C0R135G for a thousand dollar bill real?

Without more information, e.g. the bill's date, it's difficult to say whether the serial number is genuine. However the letter and number pattern looks very suspicious because it doesn't match any of the most common arrangements:

• Older bills' serial numbers usually consisted of a single leading letter, four or five digits, and single trailing letter.
• Later-date bills had eight digits instead of 4 or 5 but still had single letters.
• Leading double letters weren't used until 1990, decades after the $1000 denomination was discontinued.

Your best bet would be to have the bill examined in person by a banknote expert.