diff --git a/stan/math/prim/err/check_cholesky_factor.hpp b/stan/math/prim/err/check_cholesky_factor.hpp
index 099d2bc3986..2cb2c2d0db5 100644
--- a/stan/math/prim/err/check_cholesky_factor.hpp
+++ b/stan/math/prim/err/check_cholesky_factor.hpp
@@ -6,6 +6,7 @@
 #include <stan/math/prim/fun/to_ref.hpp>
 #include <stan/math/prim/fun/value_of_rec.hpp>
 #include <stan/math/prim/err/check_positive.hpp>
+#include <stan/math/prim/err/check_nonnegative.hpp>
 #include <stan/math/prim/err/check_less_or_equal.hpp>
 #include <stan/math/prim/err/check_lower_triangular.hpp>
 #include <stan/math/prim/err/make_iter_name.hpp>
@@ -34,7 +35,7 @@ inline void check_cholesky_factor(const char* function, const char* name,
                                   const Mat& y) {
   check_less_or_equal(function, "columns and rows of Cholesky factor", y.cols(),
                       y.rows());
-  check_positive(function, "columns of Cholesky factor", y.cols());
+  check_nonnegative(function, "columns of Cholesky factor", y.cols());
   auto&& y_ref = to_ref(value_of_rec(y));
   check_lower_triangular(function, name, y_ref);
   check_positive(function, name, y_ref.diagonal());
diff --git a/test/unit/math/prim/prob/lkj_corr_test.cpp b/test/unit/math/prim/prob/lkj_corr_test.cpp
index 220f19eb828..e379642999b 100644
--- a/test/unit/math/prim/prob/lkj_corr_test.cpp
+++ b/test/unit/math/prim/prob/lkj_corr_test.cpp
@@ -3,6 +3,19 @@
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/math/distributions.hpp>
 
+TEST(ProbDistributionsLkjCorr, testZero) {
+  boost::random::mt19937 rng;
+  unsigned int K = 0;
+  Eigen::MatrixXd Sigma(K, K);
+  Sigma.setZero();
+  Sigma.diagonal().setOnes();
+  double eta = stan::math::uniform_rng(0, 2, rng);
+  double f = stan::math::do_lkj_constant(eta, K);
+  EXPECT_FLOAT_EQ(0, stan::math::lkj_corr_cholesky_lpdf(Sigma, eta));
+  eta = 1.0;
+  EXPECT_FLOAT_EQ(0, stan::math::lkj_corr_cholesky_lpdf(Sigma, eta));
+}
+
 TEST(ProbDistributionsLkjCorr, testIdentity) {
   boost::random::mt19937 rng;
   unsigned int K = 4;