Yes. Modern firearms must have a serial number. I am not sure if the serial number has to be visible. It could have been inside the mechanism. However, it could also have been a set up for arrest if they told you it had no serial number, or you caught it, and they still wanted to sell it to you, since the law says "knowingly."
I think this is up to date:
E. PROHIBITED FIREARMS & AMMO
1. National Firearms Act – A person who intends to make, receive or possess any of the following NFA firearms must first pay a tax and have the firearm registered with the Federal government (ATF): 26 U.S.C. §§ 5801- 5872, 10 years for each violation.
Short Barrel Shotgun, barrel length less than 18 inches or overall length less than 26 inches, § 5845
Short Barrel Rifle, barrel length less than 16 inches or overall length less than 26 inches, § 5845
Silencer, 18 U.S.C. § 921 (a)(3)(C)
Destructive device, (bomb, IED, Molotov cocktail)18 U.S.C. § 921 (a)(3), (a)(4); 26 U.S.C. § 5845
Machine Gun, § 5845
(Since 1986 a person may not legally make a machine gun for himself but may legally acquire one already registered with ATF: § 922 (o), 10 years).
“Any other Weapon”, weapon capable of being concealed on the person from which a shot can be discharged via an explosive (e.g., ring gun, club gun, belt buckle gun, handlebar gun, pen gun) etc., § 5845
2. Stolen Firearms & Ammo- Illegal to steal, possess, or receive a stolen firearm or ammo, §§ 922 (i), 922(j), 922 (u), 924 (l), 924 (m), 10 years.
3. Hand Gun Armor Piercing Ammo, definition: § 921 (a)(17)(B)&(C) violations: § 922 (a)(7), (a)(8), 923(e), 929, 924 (c)(5), different penalties.
4. Undetectable Firearm - Illegal to import, make or possess – § 922 (p), 5 years.
5. Body Armor – Illegal for person previously convicted of a felony crime of violence to purchase, own or possess body armor – §§ 921 (a)(35), 931, 3 years.
6. Firearms with serial numbers removed/obliterated/altered – Illegal to knowingly possess a firearm with the serial number removed, changed, etc., § 922 (k), 5 years.