diff --git a/src/process_utility.c b/src/process_utility.c
index 4d979ee2b..be4bb4f72 100644
--- a/src/process_utility.c
+++ b/src/process_utility.c
@@ -2711,6 +2711,18 @@ process_index_start(ProcessUtilityArgs *args)
 		/* Make the RangeVar for the underlying materialization hypertable */
 		stmt->relation = makeRangeVar(NameStr(ht->fd.schema_name), NameStr(ht->fd.table_name), -1);
 	}
+	else if (TS_HYPERTABLE_HAS_COMPRESSION_ENABLED(ht))
+	{
+		/* unique indexes are not allowed on compressed hypertables*/
+		if (stmt->unique || stmt->primary || stmt->isconstraint)
+		{
+			ts_cache_release(hcache);
+			ereport(ERROR,
+					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					 errmsg("operation not supported on hypertables that have compression "
+							"enabled")));
+		}
+	}
 
 	ts_hypertable_permissions_check_by_id(ht->fd.id);
 	add_hypertable_to_process_args(args, ht);
diff --git a/tsl/test/expected/compression_ddl.out b/tsl/test/expected/compression_ddl.out
index c5712da5a..49c9e2ab7 100644
--- a/tsl/test/expected/compression_ddl.out
+++ b/tsl/test/expected/compression_ddl.out
@@ -62,6 +62,13 @@ DROP INDEX new_index;
 ALTER TABLE test1 SET (fillfactor=100);
 ALTER TABLE test1 RESET (fillfactor);
 ALTER TABLE test1 ALTER COLUMN b SET STATISTICS 10;
+-- make sure we cannot create constraints or unique indexes on compressed hypertables
+\set ON_ERROR_STOP 0
+ALTER TABLE test1 ADD CONSTRAINT c1 UNIQUE(time,i);
+ERROR:  operation not supported on hypertables that have compression enabled
+CREATE UNIQUE INDEX unique_index ON test1(time,i);
+ERROR:  operation not supported on hypertables that have compression enabled
+\set ON_ERROR_STOP 1
 --test adding boolean columns with default and not null
 CREATE TABLE records (time timestamp NOT NULL);
 SELECT create_hypertable('records', 'time');
diff --git a/tsl/test/sql/compression_ddl.sql b/tsl/test/sql/compression_ddl.sql
index 1a4cd382b..8038973ea 100644
--- a/tsl/test/sql/compression_ddl.sql
+++ b/tsl/test/sql/compression_ddl.sql
@@ -42,6 +42,12 @@ ALTER TABLE test1 SET (fillfactor=100);
 ALTER TABLE test1 RESET (fillfactor);
 ALTER TABLE test1 ALTER COLUMN b SET STATISTICS 10;
 
+-- make sure we cannot create constraints or unique indexes on compressed hypertables
+\set ON_ERROR_STOP 0
+ALTER TABLE test1 ADD CONSTRAINT c1 UNIQUE(time,i);
+CREATE UNIQUE INDEX unique_index ON test1(time,i);
+\set ON_ERROR_STOP 1
+
 --test adding boolean columns with default and not null
 CREATE TABLE records (time timestamp NOT NULL);
 SELECT create_hypertable('records', 'time');