Knight, Afghanistan or Northern India. H: 5 cm, early 6th c. AD.
(See more photographs here)

 
 7 pieces set, ivory , dated 7 to 8th c., found at Afrasiab, near Samarkand, Uzbekistan State Museum of Samarkand
Earliest known Chess pieces.

Isolated Knight found in Afrasiab, bone, 7 to 8th c?

Ivory piece most probably dated from 11th c but Linder thinks that 7 to 8th c is more accurate. Found in Saqqizabad, Iran and very similar to the Vizier of the Afrasiab set. Metropolitan Museum of Art, New York.
(Same piece on the line below)

Fil (Elephant/Bishop), origine unknown (Iran, Irak, India?), 7th-8th c.?, The Metropolitan Museum of Art

Elephant, alabaster, Nishapur (Iran), 9th c., private collection (see an older similar from Kanauj here)

 
Chariot-rook(?) from Samarkand, 7-8th c, ivory. (British Museum)

There are other Chess pieces from the same period and same origin which are very much alike Afrasiab set. Christie's action house in London has presented two pieces in April 1994. The first is a quadrige with the driver missing and might represent a Chariot or a King. The second one with only two horses might be a Vizier (?)

 
Elephant with two riders is kept by the Staatlichen Museums für Islamische Kunst in Berlin, ivory, 8th century (?)

Elephant leaning forward supporting a howdah on its back. Sold in action at Sothebys in April 2007.
 Ivory, 9th-10th century, Central Asia, Iran, Iraq (?)

Chess set found in 2006, probably coming from Afghanistan

This object has been found by Albert von Le Coq in ruin K in Gaochang (=Chotscho) (see http://en.wikipedia.org/wiki/Gaochang) and reported in his account "Koeniglich Preussische Turfan-Expeditionen" published in 1913. (check for pages 217 & 218). Gaochang is an ancient oasis of the Silk Road, 30km southeast of modern Turpan in Xinjiang, today in China. Along with that piece was found a Xiangqi Pao ! See it there. This was an active Buddhist place from 5 to 7th centuries.

 Knight (?), Egypt, 7th-8th century, wood, Rogers Fund, The Metropolitan Museum of Art

Rukh or Knight, origin unknown, 11th-12th c., carved ivory
The Metropolitan Museum of Art

Chess piece said to be a King from Egypt, Islamic period. I agree with Manfred Eder who doubts and draw attention to the resemblence with an Indian piece (see there)

Elephant said to be Byzantine art. Found in Iraq, from 10th c. e
Museo Bargello, Florence, Italy

Rock crystal, 800 AD. Found at Basra, South Iraq.

Persian Bronze, 6th-7th AD.

Rook, Western Islamic Lands, 7th-8th c., ivory, Pfeifer Fund, The Metropolitan Museum Of Art
A design between figurative and abstract!

Bishop, Western Islamic Lands, 8th-10th c., ivory, Pfeifer Fund, The Metropolitan Museum Of Art 

Rukh, Western Islamic Lands, 8th-10th c., ivory
The Metropolitan Museum Of Art

Shah, Iran, 8th-10th c., carved jet
The Metropolitan Museum Of Art 

Iranian Rook from Nishapur, 9th c.

Knight, wood with inlay of bone or ivory,Egypt, 9-10th c.
Staatliche Museen zu Berlin, Museum für Islamische Kunst

Chess piece (?) in glass, Lebanon, 10th c.

Chess Pawn (?), Western Islamic Lands, glass, 8th-11th c., Pfeiffer Fund,
The Metropolitan Museum Of Art

Muslim King or Vizir, ivory
9th c., Monnaies, Médailles et Antiques (coll. Froehner, n° 9043), Paris

Chess piece, Egypt, 10-11th c

King, ivory with inlays of lead, Sicily, 11-12th c.
Staatliche Museen zu Berlin, Museum für Islamische Kunst

King or Vizir, ivory, Syria or Iran, 9-12th c.
Private collection 

Rook, ivory, Syria or Iran, 9-12th c.
Private collection

Chess piece, rock crystal, Egypt, 10-11th c.,
Staatliche Museen zu Berlin, Museum für Islamische Kunst

Chess pieces, Egypt, 10-12th c. (British Museum)

Rook, said to be Byzantine art,
Museo Bargello, Florence, Italy   

Large Persian terracotta piece circa 1000 - 1100 A.D. 
(A Vizir? Only remaining piece from this particular set)

Rooks, green glazed pottery, Iran, private collection

Shah / Shah / Rukh / Fil

Nishapur pieces, Tepe Madrasa, Iran, beg. 9th century
ivory with traces of green, The Metropolitan Museum Of Art. 

Another Nishapur set, Iran, 12th century, composite body, glazed
unique almost complete set from the Seljuk period
The Metropolitan Museum of Art

Rook, Egypt, Islamic period. (I can't remember where I took this image but it looks very similar to the Iraqian Rook here below)

Shah, Egypt or Syria, Mamluk period, 13th-14th c., glass
The Metropolitan Museum of Art 

 From a Byzantin wreck, wood?, Serçe Limani, Anatolian coast (Turkey), 11th c.

  
Pawn, Shah, Vizir, Knights and Rook, Arabic chess set, Rock-crystal and smoken topaz, 13th.c,
Topkapi Palace Museum, Istanbul, Turkiye