According to Space News, Czech deputy prime minister Pavel Bělobrádek (Whitebearded Paul, Christian Democrats, the smallest coalition party – here is why the party isn't larger, those 16% thought that they were asked about Godly Karel Gott) impressed his hosts at the Kennedy Space Center by an excellent idea almost no one in our homeland has heard yet: Czechia should establish its own space research center. At €15 million per year, Czechia's contributions to ESA belong among 3 post-communist countries' funds above €5 million.
Czechia was the third country to land humans at another planet. Note that in late 1992, they used the identical flag to the Polish one – it was believed that we wouldn't be able to steal the blue Slovak wedge and keep the Czechoslovak flag. These astronauts were caught by UFOyaga (just when Ms Tereshkova was being grilled) who wanted to devour them for her dinner but thanks to the Biostar from the U.S. spaceship, two of the Czech astronauts were able to escape and return to the Earth.
I am not sure how important and healthy our space program is right now. But there's some tradition to build upon, of course.
The beginnings were modest. 55 years ago, the Czech cultural elite created the song Honor to the Astronaut (Good Morning, Major Gagarin). They were actually using the word astronaut for Gagarin for quite some time before the Russian counterpart cosmonaut won the battle.
Because we were the most cordial friends of the Soviet Union ;-), or at least this is what we were taught (and my visit to Sverdlovsk in 1988 was compatible with that claim), Czechoslovakia was the first foreign country that Gagarin visited after he returned to Earth.
In 1978, Czechoslovakia became the third country in the world that has sent a human to space. It was Vladimír Remek, later a member of the European Parliament and the current Czech ambassador to Russia. He flew aboard Soyuz 28 along with Alexei Gubarev (USSR).
Remek was finally chosen as the most politically correct choice. His father was a Slovak pilot, his mother was Czech. In an interview, Remek has claimed that he was a true national hero because he was the first person who has smuggled alcohol to outer space. However, the beginnings were modest. He only managed to smuggle 0.04 liters of an illegal cognac which had to be enough for 6 people and for 3 months. He's still angry that he failed to bring lots of beer to the spaceship illegally.
In a Beer Nation, everything is about beer. The space research cannot be an exception. Before he flew, Remek had the duty to lose 12 kilograms of weight. He was asked about his secret weight loss formula, of course. The only functional formula says "start eating, stop gorging". ;-)
Czechoslovakia has also launched several satellites, first designer around 1973. All of them were launched from the Plesetsk Cosmodrome, the largest Soviet cosmodrome (larger than Baikonur) that was secret for quite some time. Magion 1,2,3,4,5 were launched in 1978, 1982, 1991, 1995, and 1996, respectively. These probes were made by geophysicists and IT folks at the Academy of Sciences. Mag-ion indicates that they investigated the magnetic field, ionosphere, and plasma around the Earth. Magion 5 – almost identical to Magion 4 – looked dead after a few hours but 2 years later, it was miraculously fixed, probably by the solar radiation that melted some shorted wires away.
Czechoslovakia used to be active in the international Intercosmos program. In the period up to 1978, a whopping 45% of the experiment in this program were Czechoslovak experiments. As far as I can see, after 1996, the activity of the Czech space program has dropped to infinitesimal numbers. Another probe called MIMOSA sent in 2003 failed to fulfill its mission due to problems after it was launched. It was supposed to measure the atmosphere using some microaccelerometer, whatever the exact idea was, but exactly this microaccelerometer MACEK failed to get de-arrested.
The only other major Czech products in space, as far as I know, were the Little Mole, who is now a dual Czech-Chinese citizen along with his spouse, a panda, and Antonín Dvořák's New World Symphony that was played by Neil Armstrong on the Moon.
But Whitebearded Paul's vague remarks at the Kennedy Space Center could be the first steps towards some Czech Starshot, of course. ;-)