diff --git a/stan/math/prim/functor/reduce_sum_static.hpp b/stan/math/prim/functor/reduce_sum_static.hpp
index 7ad8648aad8..09d570fa20e 100644
--- a/stan/math/prim/functor/reduce_sum_static.hpp
+++ b/stan/math/prim/functor/reduce_sum_static.hpp
@@ -50,9 +50,9 @@ inline auto reduce_sum_static(Vec&& vmapped, int grainsize, std::ostream* msgs,
 
 #ifdef STAN_THREADS
   return internal::reduce_sum_impl<ReduceFunction, void, return_type, Vec,
-                                   Args...>()(std::forward<Vec>(vmapped), false,
-                                              grainsize, msgs,
-                                              std::forward<Args>(args)...);
+                                   ref_type_t<Args&&>...>()(
+      std::forward<Vec>(vmapped), false, grainsize, msgs,
+      std::forward<Args>(args)...);
 #else
   if (vmapped.empty()) {
     return return_type(0);
diff --git a/test/unit/math/prim/functor/reduce_sum_static_expression_test.cpp b/test/unit/math/prim/functor/reduce_sum_static_expression_test.cpp
new file mode 100644
index 00000000000..e44bb64e8f1
--- /dev/null
+++ b/test/unit/math/prim/functor/reduce_sum_static_expression_test.cpp
@@ -0,0 +1,67 @@
+#include <stan/math.hpp>
+#include <gtest/gtest.h>
+
+#include <atomic>
+#include <vector>
+
+namespace stan {
+namespace math {
+namespace test {
+
+// Counts how many times the expression's coefficients are read.
+template <typename T>
+struct counting_op {
+  std::atomic<int>* count_;
+
+  explicit counting_op(std::atomic<int>* count) : count_(count) {}
+
+  inline const T& operator()(const T& a) const {
+    ++(*count_);
+    return a;
+  }
+};
+
+struct expression_sum_lpdf {
+  template <typename VecT, typename EigExpr>
+  inline auto operator()(const VecT& sub_slice, std::size_t start,
+                         std::size_t end, std::ostream* msgs,
+                         const EigExpr& shared) const {
+    // Read the expression once per call so the counter tracks calls, not terms.
+    stan::return_type_t<VecT, EigExpr> shared_sum = stan::math::sum(shared);
+    stan::return_type_t<VecT, EigExpr> sum = 0;
+    for (std::size_t i = 0; i < sub_slice.size(); ++i) {
+      sum += sub_slice[i] * shared_sum;
+    }
+    return sum;
+  }
+};
+
+}  // namespace test
+}  // namespace math
+}  // namespace stan
+
+// https://github.com/stan-dev/math/issues/3304
+TEST(StanMathPrim_reduce_sum_static, eigen_expression_arg_evaluated_once) {
+  using stan::math::test::counting_op;
+  using stan::math::test::expression_sum_lpdf;
+
+  Eigen::MatrixXd m = Eigen::MatrixXd::Ones(2, 2);
+  std::vector<double> slice{1.0, 2.0, 3.0, 4.0};
+
+  std::atomic<int> reduce_sum_count{0};
+  counting_op<double> op_dynamic(&reduce_sum_count);
+  double from_reduce_sum = stan::math::reduce_sum<expression_sum_lpdf>(
+      slice, 1, nullptr, m.block(0, 0, 1, 1).unaryExpr(op_dynamic));
+
+  std::atomic<int> reduce_sum_static_count{0};
+  counting_op<double> op_static(&reduce_sum_static_count);
+  double from_reduce_sum_static
+      = stan::math::reduce_sum_static<expression_sum_lpdf>(
+          slice, 1, nullptr, m.block(0, 0, 1, 1).unaryExpr(op_static));
+
+  EXPECT_DOUBLE_EQ(from_reduce_sum, 10.0);
+  EXPECT_DOUBLE_EQ(from_reduce_sum_static, 10.0);
+
+  EXPECT_EQ(1, reduce_sum_count.load());
+  EXPECT_EQ(1, reduce_sum_static_count.load());
+}
diff --git a/test/unit/math/rev/functor/reduce_sum_static_expression_test.cpp b/test/unit/math/rev/functor/reduce_sum_static_expression_test.cpp
new file mode 100644
index 00000000000..317406cbc90
--- /dev/null
+++ b/test/unit/math/rev/functor/reduce_sum_static_expression_test.cpp
@@ -0,0 +1,45 @@
+#include <stan/math/rev.hpp>
+#include <test/unit/math/rev/util.hpp>
+#include <gtest/gtest.h>
+
+#include <vector>
+
+namespace stan {
+namespace math {
+namespace test {
+
+struct expression_sum_lpdf {
+  template <typename VecT, typename EigExpr>
+  inline auto operator()(const VecT& sub_slice, std::size_t start,
+                         std::size_t end, std::ostream* msgs,
+                         const EigExpr& shared) const {
+    stan::math::var sum = 0;
+    for (std::size_t i = 0; i < sub_slice.size(); ++i) {
+      sum += sub_slice[i] * stan::math::sum(shared);
+    }
+    return sum;
+  }
+};
+
+}  // namespace test
+}  // namespace math
+}  // namespace stan
+
+// https://github.com/stan-dev/math/issues/3304
+TEST_F(AgradRev, StanMathRev_reduce_sum_static_eigen_expression_arg_gradient) {
+  using stan::math::var;
+  using stan::math::test::expression_sum_lpdf;
+
+  Eigen::Matrix<var, -1, -1> m = Eigen::MatrixXd::Ones(2, 2);
+  std::vector<var> slice{1.0, 2.0, 3.0, 4.0};
+
+  var out = stan::math::reduce_sum_static<expression_sum_lpdf>(
+      slice, 1, nullptr,
+      m.block(0, 0, 1, 1).unaryExpr([](const var& a) { return a; }));
+
+  EXPECT_DOUBLE_EQ(10.0, out.val());
+
+  out.grad();
+  EXPECT_DOUBLE_EQ(10.0, m(0, 0).adj());
+  EXPECT_DOUBLE_EQ(1.0, slice[0].adj());
+}