diff --git a/CHANGELOG.md b/CHANGELOG.md
index a0db2221..36aafb24 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,8 @@
 # SparseConnectivityTracer.jl
 
+## Unreleased
+* ![Feature][badge-feature] Add support for `cholesky` ([#322])
+
 ## Version `v1.2.1`
 * ![Bugfix][badge-bugfix] Fix `NaNMath.pow` method ambiguity ([#292])
 
@@ -166,6 +169,7 @@ This release is only breaking for users who touched unexported internals.
 [badge-maintenance]: https://img.shields.io/badge/maintenance-gray.svg
 [badge-docs]: https://img.shields.io/badge/docs-orange.svg
 
+[#322]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/322
 [#292]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/292
 [#290]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/290
 [#289]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/289
diff --git a/src/overloads/arrays.jl b/src/overloads/arrays.jl
index b8068544..41ba5453 100644
--- a/src/overloads/arrays.jl
+++ b/src/overloads/arrays.jl
@@ -72,6 +72,31 @@ function LinearAlgebra.eigen(
     return LinearAlgebra.Eigen(values, vectors)
 end
 
+## Cholesky
+# A generic `cholesky` compares matrix entries (pivoting / positive-definiteness), which on tracers
+# return a tracer rather than a `Bool`. Like `eigen`, return a conservative all-depends factor.
+function LinearAlgebra.cholesky(
+        A::AbstractMatrix{T},
+        ::LinearAlgebra.NoPivot = LinearAlgebra.NoPivot();
+        check::Bool = true,
+    ) where {T <: AbstractTracer}
+    LinearAlgebra.checksquare(A)
+    n = size(A, 1)
+    t = second_order_or(A)
+    return LinearAlgebra.Cholesky(Fill(t, n, n), 'U', 0)
+end
+function LinearAlgebra.cholesky(
+        A::AbstractMatrix{T},
+        ::LinearAlgebra.RowMaximum;
+        tol::Real = 0.0,
+        check::Bool = true,
+    ) where {T <: AbstractTracer}
+    LinearAlgebra.checksquare(A)
+    n = size(A, 1)
+    t = second_order_or(A)
+    return LinearAlgebra.CholeskyPivoted(Fill(t, n, n), 'U', 1:n, n, tol, 0)
+end
+
 ## Inverse
 function Base.inv(A::StridedMatrix{T}) where {T <: AbstractTracer}
     LinearAlgebra.checksquare(A)
diff --git a/test/test_arrays.jl b/test/test_arrays.jl
index 6eb8d102..bbba8acf 100644
--- a/test/test_arrays.jl
+++ b/test/test_arrays.jl
@@ -12,6 +12,7 @@ using Test
 using LinearAlgebra: Symmetric, Diagonal, diagind
 using LinearAlgebra: det, logdet, logabsdet, norm, opnorm
 using LinearAlgebra: eigen, eigmax, eigmin
+using LinearAlgebra: cholesky, NoPivot, RowMaximum
 using LinearAlgebra: inv, pinv, dot
 using SparseArrays: sparse, spdiagm
 
@@ -697,6 +698,21 @@ end
     @test all(t -> sameidx(t, s_out), vectors)
 end
 
+@testset "Cholesky" begin
+    t1 = idx2tracer([1, 3, 4])
+    t2 = idx2tracer([2, 4])
+    t3 = idx2tracer([8, 9])
+    t4 = idx2tracer([8, 9])
+    A = [t1 t2; t3 t4]
+    s_out = idx2set([1, 2, 3, 4, 8, 9])
+    @testset "$pivot" for pivot in (NoPivot(), RowMaximum())
+        factors = cholesky(A, pivot).factors
+        @test size(factors) == (2, 2)
+        @test all(t -> sameidx(t, s_out), factors)
+    end
+    @test all(t -> sameidx(t, s_out), cholesky(A).factors)
+end
+
 @testset "SparseMatrixCSC construction" begin
     t1 = idx2tracer(1)
     t2 = idx2tracer(2)