  In the representation theory of finite groups, there is a well-known and
important conjecture due to M. Brou\'e. He conjectures that, for any prime p,
if a p-block A of a finite group G has an abelian defect group P, then A and
its Brauer corresponding block A_N of the normaliser N_G(P) of P in G are
derived equivalent (Rickard equivalent). This conjecture is called Strong
Version of Brou\'e's Abelian Defect Group Conjecture. In this paper, we prove
that the strong version of Brou\'e's abelian defect group conjecture is true
for the non-principal 2-block A with an elementary abelian defect group P of
order 8 of the sporadic simple Conway group Co_3. This result completes the
verification of the strong version of Brou\'e's abelian defect group conjecture
for all primes p and for all p-blocks of Co_3.
