diff --git a/src/stan/analyze/mcmc/check_chains.hpp b/src/stan/analyze/mcmc/check_chains.hpp
index 6f816982b3f..2c3144a1c3f 100644
--- a/src/stan/analyze/mcmc/check_chains.hpp
+++ b/src/stan/analyze/mcmc/check_chains.hpp
@@ -17,9 +17,12 @@ namespace analyze {
  * @param chains matrix of draws, one column per chain
  * @return bool true if OK, false otherwise
  */
-inline bool is_finite_and_varies(const Eigen::MatrixXd chains) {
+inline bool is_finite_and_varies(const Eigen::MatrixXd& chains) {
   size_t num_chains = chains.cols();
   size_t num_samples = chains.rows();
+  if (num_samples < 2) {
+    return false;
+  }
   Eigen::VectorXd first_draws = Eigen::VectorXd::Zero(num_chains);
   for (std::size_t i = 0; i < num_chains; ++i) {
     first_draws(i) = chains.col(i)(0);
diff --git a/src/stan/analyze/mcmc/ess.hpp b/src/stan/analyze/mcmc/ess.hpp
index 33342ce68a8..56490919624 100644
--- a/src/stan/analyze/mcmc/ess.hpp
+++ b/src/stan/analyze/mcmc/ess.hpp
@@ -28,6 +28,10 @@ namespace analyze {
 double ess(const Eigen::MatrixXd& chains) {
   const Eigen::Index num_chains = chains.cols();
   const Eigen::Index draws_per_chain = chains.rows();
+  if (draws_per_chain < 4) {
+    return std::numeric_limits<double>::quiet_NaN();
+  }
+
   Eigen::MatrixXd acov(draws_per_chain, num_chains);
   Eigen::VectorXd chain_mean(num_chains);
   Eigen::VectorXd chain_var(num_chains);
diff --git a/src/stan/analyze/mcmc/mcse.hpp b/src/stan/analyze/mcmc/mcse.hpp
index b859cfa32c4..9bcfafc868a 100644
--- a/src/stan/analyze/mcmc/mcse.hpp
+++ b/src/stan/analyze/mcmc/mcse.hpp
@@ -39,9 +39,9 @@ inline double mcse_mean(const Eigen::MatrixXd& chains) {
  * @return mcse
  */
 inline double mcse_sd(const Eigen::MatrixXd& chains) {
-  if (chains.rows() < 4 || !is_finite_and_varies(chains))
+  if (chains.rows() < 8 || !is_finite_and_varies(chains)) {
     return std::numeric_limits<double>::quiet_NaN();
-
+  }
   // center the data, take abs value
   Eigen::MatrixXd draws_ctr = (chains.array() - chains.mean()).abs().matrix();