We prove a combinatorial formula for the Macdonald polynomial
H
~
μ
(
x
;
q
,
t
)
\tilde {H}_{\mu }(x;q,t)
which had been conjectured by Haglund. Corollaries to our main theorem include the expansion of
H
~
μ
(
x
;
q
,
t
)
\tilde {H}_{\mu }(x;q,t)
in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schützenberger for Hall-Littlewood polynomials, a new proof of Knop and Sahi’s combinatorial formula for Jack polynomials as well as a lifting of their formula to integral form Macdonald polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients
K
~
λ
μ
(
q
,
t
)
\tilde {K}_{\lambda \mu }(q,t)
in the case that
μ
\mu
is a partition with parts
≤
2
\leq 2
.