  A tri-colored sum-free set in an abelian group $H$ is a collection of ordered
triples in $H^3$, $\{(a_i,b_i,c_i)\}_{i=1}^m$, such that the equation
$a_i+b_j+c_k=0$ holds if and only if $i=j=k$. Using a variant of the lemma
introduced by Croot, Lev, and Pach in their breakthrough work on
arithmetic-progression-free sets, we prove that the size of any tri-colored
sum-free set in $\mathbb{F}_2^n$ is bounded above by $6 {n \choose \lfloor n/3
\rfloor}$. This upper bound is tight, up to a factor subexponential in $n$:
there exist tri-colored sum-free sets in $\mathbb{F}_2^n$ of size greater than
${n \choose \lfloor n/3 \rfloor} \cdot 2^{-\sqrt{16 n / 3}}$ for all
sufficiently large $n$.
