diff --git a/pkg/chunkenc/gzip.go b/pkg/chunkenc/gzip.go
index efbad487ce..8dc8a01bc4 100644
--- a/pkg/chunkenc/gzip.go
+++ b/pkg/chunkenc/gzip.go
@@ -18,6 +18,8 @@ import (
 	"github.com/pkg/errors"
 )
 
+const blocksPerChunk = 10
+
 var (
 	magicNumber = uint32(0x12EE56A)
 
@@ -307,12 +309,20 @@ func (c *MemChunk) Size() int {
 
 // SpaceFor implements Chunk.
 func (c *MemChunk) SpaceFor(*logproto.Entry) bool {
-	return len(c.blocks) < 10
+	return len(c.blocks) < blocksPerChunk
 }
 
 // Append implements Chunk.
 func (c *MemChunk) Append(entry *logproto.Entry) error {
-	return c.head.append(entry.Timestamp.UnixNano(), entry.Line)
+	if err := c.head.append(entry.Timestamp.UnixNano(), entry.Line); err != nil {
+		return err
+	}
+
+	if c.head.size >= c.blockSize {
+		return c.cut()
+	}
+
+	return nil
 }
 
 // Close implements Chunk.
@@ -341,6 +351,7 @@ func (c *MemChunk) cut() error {
 
 	c.head.entries = c.head.entries[:0]
 	c.head.mint = 0 // Will be set on first append.
+	c.head.size = 0
 
 	return nil
 }
diff --git a/pkg/chunkenc/gzip_test.go b/pkg/chunkenc/gzip_test.go
index c316094bf9..0f6f0e80e4 100644
--- a/pkg/chunkenc/gzip_test.go
+++ b/pkg/chunkenc/gzip_test.go
@@ -172,6 +172,41 @@ func TestGZIPSerialisation(t *testing.T) {
 	require.True(t, bytes.Equal(byt, byt2))
 }
 
+func TestGZIPChunkFilling(t *testing.T) {
+	chk := NewMemChunk(EncGZIP)
+	chk.blockSize = 1024
+
+	// We should be able to append only 10KB of logs.
+	maxBytes := chk.blockSize * blocksPerChunk
+	lineSize := 512
+	lines := maxBytes / lineSize
+
+	logLine := string(make([]byte, lineSize))
+	entry := &logproto.Entry{
+		Timestamp: time.Unix(0, 0),
+		Line:      logLine,
+	}
+
+	i := int64(0)
+	for ; chk.SpaceFor(entry) && i < 30; i++ {
+		entry.Timestamp = time.Unix(0, i)
+		require.NoError(t, chk.Append(entry))
+	}
+
+	require.Equal(t, int64(lines), i)
+
+	it, err := chk.Iterator(time.Unix(0, 0), time.Unix(0, 100), logproto.FORWARD)
+	require.NoError(t, err)
+	i = 0
+	for it.Next() {
+		entry := it.Entry()
+		require.Equal(t, i, entry.Timestamp.UnixNano())
+		i++
+	}
+
+	require.Equal(t, int64(lines), i)
+}
+
 func logprotoEntry(ts int64, line string) *logproto.Entry {
 	return &logproto.Entry{
 		Timestamp: time.Unix(0, ts),