Despite the current lack of a science-based tag you clearly use the phrase "scientifically possible" so for a science based answer:
No, unless maybe the planet had
- no atmosphere,
- no liquid (which would evaporate in the absence of an atmosphere),
- no vulcanism,
- no radioactivity
- was artificially constructed from an extremely small number of elements
- with an asteroid shield
- and a radiation shield
- and a maintenance crew that hid any material that had a defect or fracture.
As noted by others, white light is composed of various colours of light. If the incoming light isn't white then from the offset everything is coloured other than shades of grey.
The only atmosphere that won't Rayleigh scatter light is the complete absence of atmosphere. Even at the top of Everest or in commercial airlines where air is too thin to provide a breathable oxygen content the sky is blue due to differntuial scattering of incoming white light. Dust storms will make the atmosphere appear red as will sunsets. Your planet would have to have no atmosphere or an atmosphere so thin as to be invisible and unable to suspend atmospheric dust and suspended water wouldn't be allowed to prevent rainbows.
Liquids in general would have to be eliminated as they are prone to similar colouring effects and they also absorb various wavelengths of light. Suspended particles can shift the colour spectrum as well.
For things to appear in shades of grey to a human there must either be low light so human colour sense doesn't work or everything on the planet's components must be only black and white.
The former is meaningless as humans supply their own light sources. This means the latter must be the case in order for the original proposition to be true.
Since you're talking about a planet with a surface you're referencing a terrestrial planet. The surface of terrestrial planets are made largely of rocks which are themselves made of minerals and fragments of other rocks. Such a planet would have to have to have formed from no almost no transition elements as transition elements often form colourful compounds. You'd have no gold, copper, iron, manganese, chromium, silver, etc, which aside from making many pretty colours are also useful for industrial purposes. Since planets are formed from star-stuff and stars inherently go about making transition elements this is all but impossible. The planet would have to be artificially constructed to avoid these.
Your planet would have to be shielded from asteroids/meteors as many of these are made from transitions elements and over geologic time you can expect substantial numbers of these to impact a planet.
Radiation shielding would be required to prevent radiation from initiating nuclear changes that could result in the formation of transition elements. This would also necessitate the planet being made from only non-radioactive isotopes to prevent them decaying into colour-producing transition elements. Radiation can also effect colour changes, such as causing quartz, clear and colourless, to be converted to smoky quartz, clear and brown.
However, transition elements are not the only things that produce colour. Other elements are also coloured such as sulphur, chlorine, iodine, bromine, fluorine and these often produce coloured compounds. Minerals can also change colour through tenebrescence. And normally colourless elements can also form coloured substances, such as sugar solutions in water.
All the discussion on minerals above involves colour centres, regions in the solid where incoming photons interact with the electron stucture of the material but there are other mechanisms such as rainbow-like inteference patterns seen when stones have an internal fracture. These are actually also visible when fractures occur near the surface of otherwise opaque rocks, including obsidian which is opaque and black. Rainbows have been mentioned but one also needs to prevent dispersion through other clear materials such as occurs in prisms.
Vulcanism isn't allowed simply because molten rock glows red.
The only way around this is to have manufactured the planet from a limited number of materials that are not coloured and which are maintained to prevent the formation of colour.