diff --git a/Project.toml b/Project.toml
index 4cf597727..fe512f136 100644
--- a/Project.toml
+++ b/Project.toml
@@ -28,8 +28,15 @@ SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 TruncatedStacktraces = "781d530d-4396-4725-bb49-402e4bee1e77"
 
+[weakdeps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
+[extensions]
+SciMLBaseChainRulesCoreExt = "ChainRulesCore"
+
 [compat]
 ArrayInterface = "6, 7"
+ChainRulesCore = "1.15"
 CommonSolve = "0.2"
 ConstructionBase = "1"
 DocStringExtensions = "0.8, 0.9"
@@ -51,6 +58,7 @@ TruncatedStacktraces = "1"
 julia = "1.6"
 
 [extras]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 DelayDiffEq = "bcd4f6db-9728-5f36-b5f7-82caef46ccdb"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
@@ -60,4 +68,4 @@ StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Pkg", "SafeTestsets", "Test", "StaticArrays"]
+test = ["Pkg", "SafeTestsets", "Test", "StaticArrays", "ChainRulesCore"]
diff --git a/ext/SciMLBaseChainRulesCoreExt.jl b/ext/SciMLBaseChainRulesCoreExt.jl
new file mode 100644
index 000000000..e71390ef3
--- /dev/null
+++ b/ext/SciMLBaseChainRulesCoreExt.jl
@@ -0,0 +1,35 @@
+module SciMLBaseChainRulesCoreExt
+
+using SciMLBase
+isdefined(Base, :get_extension) ? (import ChainRulesCore) : (import ..ChainRulesCore)
+
+function ChainRulesCore.rrule(::Type{
+                                     <:SciMLBase.PDETimeSeriesSolution{T, N, uType, Disc, Sol, DType, tType, domType, ivType, dvType,
+                                     P, A,
+                                     IType}}, u,
+                              args...) where {T, N, uType, Disc, Sol, DType, tType, domType, ivType, dvType,
+                              P, A,
+                              IType}
+    function PDETimeSeriesSolutionAdjoint(ȳ)
+        (NoTangent(), ȳ, ntuple(_ -> NoTangent(), length(args))...)
+    end
+
+    SciMLBase.PDETimeSeriesSolution{T, N, uType, Disc, Sol, DType, tType, domType, ivType, dvType,
+    P, A,
+    IType}(u, args...), PDETimeSeriesSolutionAdjoint
+end
+
+function ChainRulesCore.rrule(::Type{
+                                     <:SciMLBase.PDENoTimeSolution{T, N, uType, Disc, Sol, domType, ivType, dvType, P, A,
+                                     IType}}, u,
+                              args...) where {T, N, uType, Disc, Sol, domType, ivType, dvType, P, A,
+                              IType}
+    function PDENoTimeSolutionAdjoint(ȳ)
+        (NoTangent(), ȳ, ntuple(_ -> NoTangent(), length(args))...)
+    end
+
+    SciMLBase.PDENoTimeSolution{T, N, uType, Disc, Sol, domType, ivType, dvType, P, A,
+    IType}(u, args...), PDENoTimeSolutionAdjoint
+end
+
+end
diff --git a/src/SciMLBase.jl b/src/SciMLBase.jl
index 69e4e0699..e743fcd64 100644
--- a/src/SciMLBase.jl
+++ b/src/SciMLBase.jl
@@ -748,6 +748,12 @@ function wrapfun_oop end
 function wrapfun_iip end
 function unwrap_fw end
 
+@static if !isdefined(Base, :get_extension)
+    function __init__()
+        @require ChainRulesCore="d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" begin include("../ext/SciMLBaseChainRulesCore.jl") end
+    end
+end
+
 export ReturnCode
 
 export DEAlgorithm, SciMLAlgorithm, DEProblem, DEAlgorithm, DESolution, SciMLSolution