diff --git a/tsdb/chunks/chunks.go b/tsdb/chunks/chunks.go
index 418541f58..1a11924d1 100644
--- a/tsdb/chunks/chunks.go
+++ b/tsdb/chunks/chunks.go
@@ -456,16 +456,14 @@ func (b realByteSlice) Sub(start, end int) ByteSlice {
 type Reader struct {
 	// The underlying bytes holding the encoded series data.
 	// Each slice holds the data for a different segment.
-	bs    []ByteSlice
-	cs    []io.Closer // Closers for resources behind the byte slices.
-	size  int64       // The total size of bytes in the reader.
-	pool  chunkenc.Pool
-	crc32 hash.Hash
-	buf   [binary.MaxVarintLen32]byte
+	bs   []ByteSlice
+	cs   []io.Closer // Closers for resources behind the byte slices.
+	size int64       // The total size of bytes in the reader.
+	pool chunkenc.Pool
 }
 
 func newReader(bs []ByteSlice, cs []io.Closer, pool chunkenc.Pool) (*Reader, error) {
-	cr := Reader{pool: pool, bs: bs, cs: cs, crc32: newCRC32()}
+	cr := Reader{pool: pool, bs: bs, cs: cs}
 	var totalSize int64
 
 	for i, b := range cr.bs {
@@ -541,6 +539,7 @@ func (s *Reader) Chunk(ref uint64) (chunkenc.Chunk, error) {
 		// Get the lower 4 bytes.
 		// These contain the segment offset where the data for this chunk starts.
 		chkStart = int((ref << 32) >> 32)
+		chkCRC32 = newCRC32()
 	)
 
 	if sgmIndex >= len(s.bs) {
@@ -569,12 +568,12 @@ func (s *Reader) Chunk(ref uint64) (chunkenc.Chunk, error) {
 		return nil, errors.Errorf("segment doesn't include enough bytes to read the chunk - required:%v, available:%v", chkEnd, sgmBytes.Len())
 	}
 
-	sum := sgmBytes.Range(chkEnd-crc32.Size, chkEnd)
-	s.crc32.Reset()
-	if _, err := s.crc32.Write(sgmBytes.Range(chkEncStart, chkDataEnd)); err != nil {
+	sum := sgmBytes.Range(chkDataEnd, chkEnd)
+	if _, err := chkCRC32.Write(sgmBytes.Range(chkEncStart, chkDataEnd)); err != nil {
 		return nil, err
 	}
-	if act := s.crc32.Sum(s.buf[:0]); !bytes.Equal(act, sum) {
+
+	if act := chkCRC32.Sum(nil); !bytes.Equal(act, sum) {
 		return nil, errors.Errorf("checksum mismatch expected:%x, actual:%x", sum, act)
 	}
 
diff --git a/tsdb/db_test.go b/tsdb/db_test.go
index 1168460ec..70d79118f 100644
--- a/tsdb/db_test.go
+++ b/tsdb/db_test.go
@@ -25,6 +25,7 @@ import (
 	"path/filepath"
 	"sort"
 	"strconv"
+	"sync"
 	"testing"
 	"time"
 
@@ -2485,9 +2486,9 @@ func TestDBReadOnly_FlushWAL(t *testing.T) {
 	testutil.Equals(t, 1000.0, sum)
 }
 
-// TestChunkWriter ensures that chunk segment are cut at the set segment size and
+// TestChunkWriter_ReadAfterWrite ensures that chunk segment are cut at the set segment size and
 // that the resulted segments includes the expected chunks data.
-func TestChunkWriter(t *testing.T) {
+func TestChunkWriter_ReadAfterWrite(t *testing.T) {
 	chk1 := tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 1}})
 	chk2 := tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 2}})
 	chk3 := tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 3}})
@@ -2611,22 +2612,19 @@ func TestChunkWriter(t *testing.T) {
 	for i, test := range tests {
 		t.Run(strconv.Itoa(i), func(t *testing.T) {
 
-			tmpdir, err := ioutil.TempDir("", "test_chunk_witer")
+			tempDir, err := ioutil.TempDir("", "test_chunk_writer")
 			testutil.Ok(t, err)
-			defer func() {
-				testutil.Ok(t, os.RemoveAll(tmpdir))
-			}()
+			defer func() { testutil.Ok(t, os.RemoveAll(tempDir)) }()
 
-			chunkw, err := chunks.NewWriterWithSegSize(tmpdir, chunks.SegmentHeaderSize+int64(test.segmentSize))
+			chunkw, err := chunks.NewWriterWithSegSize(tempDir, chunks.SegmentHeaderSize+int64(test.segmentSize))
 			testutil.Ok(t, err)
 
 			for _, chks := range test.chks {
-				chunkw.WriteChunks(chks...)
+				testutil.Ok(t, chunkw.WriteChunks(chks...))
 			}
-
 			testutil.Ok(t, chunkw.Close())
 
-			files, err := ioutil.ReadDir(tmpdir)
+			files, err := ioutil.ReadDir(tempDir)
 			testutil.Ok(t, err)
 			testutil.Equals(t, test.expSegmentsCount, len(files), "expected segments count mismatch")
 
@@ -2655,7 +2653,7 @@ func TestChunkWriter(t *testing.T) {
 			testutil.Equals(t, sizeExp, sizeAct)
 
 			// Check the content of the chunks.
-			r, err := chunks.NewDirReader(tmpdir, nil)
+			r, err := chunks.NewDirReader(tempDir, nil)
 			testutil.Ok(t, err)
 
 			for _, chks := range test.chks {
@@ -2668,3 +2666,43 @@ func TestChunkWriter(t *testing.T) {
 		})
 	}
 }
+
+// TestChunkReader_ConcurrentReads checks that the chunk result can be read concurrently.
+// Regression test for https://github.com/prometheus/prometheus/pull/6514.
+func TestChunkReader_ConcurrentReads(t *testing.T) {
+	chks := []chunks.Meta{
+		tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 1}}),
+		tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 2}}),
+		tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 3}}),
+		tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 4}}),
+		tsdbutil.ChunkFromSamples([]tsdbutil.Sample{sample{1, 5}}),
+	}
+
+	tempDir, err := ioutil.TempDir("", "test_chunk_writer")
+	testutil.Ok(t, err)
+	defer func() { testutil.Ok(t, os.RemoveAll(tempDir)) }()
+
+	chunkw, err := chunks.NewWriter(tempDir)
+	testutil.Ok(t, err)
+
+	testutil.Ok(t, chunkw.WriteChunks(chks...))
+	testutil.Ok(t, chunkw.Close())
+
+	r, err := chunks.NewDirReader(tempDir, nil)
+	testutil.Ok(t, err)
+
+	var wg sync.WaitGroup
+	for _, chk := range chks {
+		for i := 0; i < 100; i++ {
+			wg.Add(1)
+			go func(chunk chunks.Meta) {
+				defer wg.Done()
+
+				chkAct, err := r.Chunk(chunk.Ref)
+				testutil.Ok(t, err)
+				testutil.Equals(t, chunk.Chunk.Bytes(), chkAct.Bytes())
+			}(chk)
+		}
+		wg.Wait()
+	}
+}