  Using bordered Floer theory, we construct an invariant
$\widehat{\mathit{HFO}}(Y^{\text{orb}})$ for $3$-orbifolds $Y^{\text{orb}}$
with singular set a knot that generalizes the hat flavor
$\widehat{\mathit{HF}}(Y)$ of Heegaard Floer homology for closed $3$-manifolds
$Y$. We show that for a large class of $3$-orbifolds, $\widehat{\mathit{HFO}}$
behaves like $\widehat{\mathit{HF}}$ in that $\widehat{\mathit{HFO}}$, together
with a relative $\mathbb{Z}_2$-grading, categorifies the order of
$H_1^{\text{orb}}$. When $Y^{\text{orb}}$ arises as Dehn surgery on an
integer-framed knot in $S^3$, we use the $\{-1,0,1\}$-valued knot invariant
$\varepsilon$ to determine the relationship between
$\widehat{\mathit{HFO}}(Y^{\text{orb}})$ and $\widehat{\mathit{HF}}(Y)$ of the
$3$-manifold $Y$ underlying $Y^{\text{orb}}$.
