From The Collaborative International Dictionary of English v.0.48:
Nibble \Nib"ble\, v. t. [imp. & p. p. Nibbled; p. pr. & vb. n.
Nibbling.] [Cf. Nip.]
To bite by little at a time; to seize gently with the mouth;
to eat slowly or in small bits.
Thy turfy mountains, where live nibbling sheep. --Shak.