Murray and van der Linde the two chess historians were almost certain that the birthplace of chess was Indian sub-continent, but most certainly it was invented in Iran for the following reasons: (To be brief I can outline the factors) .

1): Indian literature has no early mentions of chess but Persian literature does:
The first unmistakable reference in Sanskrit writings is in the "Harschascharita" by the court poet Bana, written between 625 and 640. On the other hand, pre-Islamic documents have solidly connected chess with the last period of the Sasanian rulers in Iran (VI-VII century). The "Kamamak", an epical treatise about the founder of this dynasty, mentions the game of chatrang as one of the accomplishments of the legendary hero. It has a proving force that a game under this name was popular in the period of redaction of the text, supposedly the end of the 6th century or the beginning of the 7th. Closely related is a shorter poem from about the same period entitled in Pahlavi "Chatrang-Nâmag", dealing with the introduction of chess in Iran.

Master Ferdowsi wrote also about it in the 11th century, but his sources are solid and form a continuous chain of witnesses going back to the middle of the 6th Century in Iran. Mater describes chess as arriving from Hind. According to historical sources this name "Hind" was not used for India until after the 11th century. Here Hind means Eastern-Province of Iranian Empire including Baluchistan, and while others thers have extended Hind to Khuzistan . As some Russian chess historians claim, nobody could possibly generate the rules of chess only by studying the array position at the beginning of a game. On the other hand, such an achievement might be made by looking at Takht-I Nard (backgammon).

2): India has no early chess pieces but Iran does:
The presence of carved chess men in Iranian domains contrasts with the absence of such items in India. There are no chess men there from early times, and only in the 10th century appears an indirect mention from al-Mas'udi: "The use of ivory (in India) is mainly directed to the carving of chess- and nard pieces". Some experts believe that old Indian chess pieces may be discovered one day! So far, this is mere speculation. The three oldest sets of chess pieces closely identified as such belong to Iranian domains, not to India. The most important are the Afrasiab pieces. They were found 1977 in Afrasiab, near Samarqand, and have been dated by its Soviet discoverers as early as the 7th-8th century. Western experts accept at least the year 761 because a coin so dated belongs to the same layer. These seven ivory men, questionable as all "idols" may be, are Iranian, even if the territory was under Islamic rule since 712. Next group of chess pieces (three chessmen) comes also from the Greater-Iran. The so-called Ferghana pieces include a "Rukh" in form of a giant bird, and its antiquity should be not too distant from the Afrasiab lot. In Nishapur another ivory set was discovered though belonging to later times, 9th or 10th century. These are not idols anymore and are carved following the abstract pattern which has been characterized as "Arabic".

3): The Arabs introduced chess in India after taking "Shatrang" from Iran:
Games upon the "ashtapada" board of 8x8, with dice and with two or more players may have served as "proto-chess", but the two types of games already differ too strongly in their nature and philosophy to make the evolution of "Chaturanga" into "Shatransh" a simple question of direct parentage via the Persian "Chatrang". Arab writers stated quite frequently that they took the game of "shatransh" from the Iranians, who called it "chatrang". This happens in the middle of a political-cultural revolution, which has been analysed in historical texts. The ruling Umayyad dynasty was thrown out after a fierce civil war by a certain Abul Abbas, who initiated a new era, founding in Baghdad in the former Iranian territory, around the year 750 and translating there from Damascus the Islamic political centre. The Abbasid dynasty was ethnically and culturally of Iranian origin. So Iranian influences became clearly dominant in the cultural renaissance which took place inside the Arabic trunk. A lot of the previous knowledge from classical Greece, Byzantium, early Egyptian and Middle East civilizations and even "from the country of Hind" was compiled and re-translated into Arabic and absorbed in a scientific body which followed its further path towards the West. Chess was only a part of this knowledge, packaged together with earlier mathematical, astronomical, philosophical or medical achievements.

However, we know that while chess flourished in Baghdad in the 9th century, the earliest reliable account of chess-playing in India date only from the 11th century.

4): Etymology is unclear:
Although, Murray shows that Pahlavi words in the game are adapted from Sanskrit, and the Arabic in turn from Pahlavi but Sanskrit closely-linked contemporary relatives such as Avestan. However, the roots of several chess terms may be so go further to India, but the fact is that the Sanskrit word "Chaturanga" means only "army", and it is unclear whether it referred to chess, to a possible form of "protochess" with four players, or to some strategically exercise with pieces over a board with military purposes.

In any case, to be on safer ground, we must remember the earliest solid evidences about the board game called chess belong to Iran. The Pahlavi word "Chatrang" means, even to- day, the mandrake plant, which has a root in form of a human figure. So, there is a good case in favour of a different etymological interpretation: Any game played with pieces representing figures may be compared with the "shatrang" plant.

Another hint is the nomenclature of the pieces, persistently related to different sorts of animals rather than to components of an army: In the "Grande Acedrex" of King Alfonso of Castile (1283) lions, crocodiles, giraffes etc. play over a board of 12x12 cases with peculiar jumping moves, and the invention of it is connected to the same remote period in India as normal chess. They are very atypical in any context referring to India. (See the reference "Hasb"(War) in "The Encyclopaedia of Islam", De Gruyter, Leyden-New York 1967). On the other hand, elephants are not at all exclusive from Indian origin (Sir William Gowers, "African Elephants and Ancient Authors", African Affairs, 47 (1948) p.173 ff. Also Frank W. Walbank, "Die Hellenistische Welt", DTV 1983 p. 205-6), not even in military campaigns: The Iranian were the first nation that introduced cavalry and they had also foot-soldiers, chariots and elephants as well as river and battle-ships. In Egypt, the Ptolemaic Kings obtained elephants regularly from Somalia. Strabo (16,4,5) mentions the foundation of several cities in Africa with the main purpose of hunting elephants. The hunters have even written dedications to Ptolemaios IV Philopator (221-204 BC). Polybios describes a battle with elephants between Ptolomaios IV and Antiochos III in 217 BC. Pyrrhus and Hannibal used it in the West. Modern research has confirmed all the details.