I will present a new method to determine quark masses from heavy-light 
meson masses.  The two theoretical foundations of the method are 
1) the well-known formula for heavy-light hadron masses in the heavy-quark
effective theory, and 2) a new definition of the heavy-quark mass with 
an elegant treatment of the renormalon problem. Using lattice-QCD data from 
the Fermilab Lattice and MILC Collaborations, the method yields precision 
on the charm and bottom quark masses comparable to the best existing 
determinations.  Using very precise quark-mass ratios, including m_c/m_s 
from this analysis, we can obtain the most precise determinations of the 
up-, down-, and strange-quark masses.