  The cosimplicial scheme $$Delta^bullet = \Delta^0 smallmatrix \to smallmatrix
\Delta^1 smallmatrix to smallmatrix ...;\quad \Delta^n
:=\Spec\Big(k[t_0,...c,t_n]/(\sum t_i -t)\Big)$$ was used in B to define higher
Chow groups. In this note, we let t tend to 0 and replace \Delta^\bullet by a
degenerate version $$Q^\bullet = Q^0 smallmatrix to smallmatrix Q^1 smallmatrix
to smallmatrix ...;\quad Q^n := \Spec\Big(k[t_0,...c,t_n]/(\sum t_i)\Big) $$ to
define an additive version of the higher Chow groups. For a field k, we show
the Chow group of 0-cycles on $Q^n$ in this theory is isomorphic to the
absolute $(n-1)$-K\"ahler forms $\Omega^{n-1}_k$.
  An analogous degeneration on the level of de Rham cohomology associated to
``constant modulus'' degenerations of varieties in various contexts is
discussed.
