diff --git a/Project.toml b/Project.toml
index e53ebb6..54e1b2e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,11 +9,22 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MKL_jll = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
+[extensions]
+FFTWChainRulesCoreExt = "ChainRulesCore"
 
 [compat]
+ChainRulesCore = "1"
 AbstractFFTs = "1.5"
 FFTW_jll = "3.3.9"
 MKL_jll = "2019.0.117, 2020, 2021, 2022, 2023"
 Preferences = "1.2"
 Reexport = "0.2, 1.0"
 julia = "1.6"
+
+[extras]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
+[weakdeps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/ext/FFTWChainRulesCoreExt.jl b/ext/FFTWChainRulesCoreExt.jl
new file mode 100644
index 0000000..789e4e9
--- /dev/null
+++ b/ext/FFTWChainRulesCoreExt.jl
@@ -0,0 +1,42 @@
+module FFTWChainRulesCoreExt
+
+using FFTW
+using FFTW: r2r
+using ChainRulesCore
+
+# DCT/IDCT
+
+for (fwd, bwd) in (
+    (dct, idct),
+    (idct, dct),
+)
+    function ChainRulesCore.frule(Δ, ::typeof(fwd), x::AbstractArray, region = 1:ndims(x))
+        Δx = Δ[2]
+        y = fwd(x, region)
+        Δy = fwd(Δx, region)
+        return y, Δy
+    end
+
+    function ChainRulesCore.rrule(::typeof(fwd), x::AbstractArray)
+        project_x = ProjectTo(x)
+        dct_pb(Δ) = NoTangent(), project_x(bwd(unthunk(Δ)))
+        return fwd(x), dct_pb
+    end
+
+    function ChainRulesCore.rrule(::typeof(fwd), x::AbstractArray, region)
+        project_x = ProjectTo(x)
+        dct_pb(Δ) = NoTangent(), project_x(bwd(unthunk(Δ), region)), NoTangent()
+        return fwd(x, region), dct_pb
+    end
+end
+
+# R2R
+
+function ChainRulesCore.frule(Δ, ::typeof(r2r), x::AbstractArray, kind, region = 1:ndims(x))
+    Δx = Δ[2]
+    y = r2r(x, kind, region)
+    Δy = r2r(Δx, kind, region)
+    return y, Δy
+end
+
+end # module
diff --git a/src/FFTW.jl b/src/FFTW.jl
index 4366ee7..82d6bde 100644
--- a/src/FFTW.jl
+++ b/src/FFTW.jl
@@ -72,4 +72,8 @@ include("dct.jl")
 include("precompile.jl")
 _precompile_()
 
+@static if !isdefined(Base, :get_extension)
+    include("../ext/FFTWChainRulesCoreExt.jl")
+end
+
 end # module
diff --git a/test/Project.toml b/test/Project.toml
index c46e7ba..a477908 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,8 +1,6 @@
-# A bug in Julia 1.6.0's Pkg causes Preferences to be dropped during `Pkg.test()`, so we work around
-# it by explicitly creating a `test/Project.toml` which will correctly communicate any preferences
-# through to the child Julia process.  X-ref: https://github.com/JuliaLang/Pkg.jl/issues/2500
-
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/runtests.jl b/test/runtests.jl
index 981f3f1..351054d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,6 @@
 # This file was formerly a part of Julia. License is MIT: https://julialang.org/license
 using FFTW
-using FFTW: fftw_provider
+using FFTW: fftw_provider, r2r
 using AbstractFFTs: Plan, plan_inv
 using Test
 using LinearAlgebra