Alvin's Hatchet is a weapon that first appeared in the episode "Alvin and the Outcasts".
Made for Alvin
After learning that the Outcasts are invading Berk, Astrid volunteers to help defend against them. Stoick then gives this axe to her despite its misshaped design do to the fire at the armory. Later, she tries to throw it at Alvin, but he somehow manages to catch it, resulting in it back in his posession.
Due to the instant in the armory, its head is misshapen and is covered in burn marks. Oddly enough, it's too small to belong to Alvin when comparing it to the size of his hand, though that may be because he was much younger when it was made for him.